I'll make these observations though and put together a potential explanation.
We start in Mark with the "woman" that anoints Jesus:
3 While He was in Bethany at the home of Simon the Leper, He was reclining at the table, and a woman came with an alabaster vial of very expensive perfume of pure nard. She broke the vial and poured the perfume over His head. 4 But there were some indignantly remarking to one another, “Why has this perfume been wasted? 5 For this perfume could have been sold for over three hundred denarii, and the money given to the poor.” And they were scolding her. 6 But Jesus said, “Leave her alone! Why are you bothering her? She has done a good deed for Me. 7 For you always have the poor with you, and whenever you want, you can do good to them; but you do not always have Me. 8 She has done what she could; she has anointed My body beforehand for the burial. 9 Truly I say to you, wherever the gospel is preached in the entire world, what this woman has done will also be told in memory of her.”
Then we have Peter's denial of Jesus:
66 And while Peter was below in the courtyard, one of the slave women of the high priest came, 67 and seeing Peter warming himself, she looked at him and said, “You were with Jesus the Nazarene as well.” 68 But he denied it, saying, “I neither know nor understand what you are talking about.” And he went out onto the porch. 69 The slave woman saw him, and began once more to say to the bystanders, “This man is one of them!” 70 But again he denied it. And after a little while the bystanders were again saying to Peter, “You really are one of them, for you are a Galilean as well.” 71 But he began to curse himself and to swear, “I do not know this man of whom you speak!” 72 And immediately a rooster crowed a second time. And Peter remembered how Jesus had made the remark to him, “Before a rooster crows twice, you will deny Me three times.” And he hurried on and began to weep.
Recall also that in Mark Peter is identified by Jesus as Satan:
But turning around and seeing His disciples, He rebuked Peter and said, “Get behind Me, Satan; for you are not setting your mind on God’s purposes, but on man’s.”
Ok, now we have to go down a bit of a rabbit hole. I think that the Gospel of Mark reflects a prior narrative about Paul. Jesus' rebuking of Peter is derived from Paul's rebuking of Peter in Galatians. But, strangely, while Jesus has called Peter Satan and Peter has denied Jesus, Mark 16 says to tell Peter of his resurrection: "Mark 16:7 But go, tell His disciples and Peter, ‘He is going ahead of you to Galilee; there you will see Him, just as He told you.’”"
This is very odd because Peter was a disciple, so by telling the disciples it would be assumed that you would tell Peter, so why name him separately?
I think because some original version of this, either written by "Mark" or a pre-Markan narrative, said to tell the disciples "and PAUL" or simply to tell Paul, not even the disciples. They don't ultimately tell Paul, because they leave afraid, but this then leads into Paul's vision of the risen Jesus. Jesus said to tell Paul, but they didn't, so Jesus came to Paul in a vision, that's the setup. Of course its also possible that it simply said to tell the disciples and made no mention of Paul. But "tell the disciples and Peter" clearly doesn't make sense.
Now, so what does this have to do with the women and the name Mary?
Mary Magdalene is not introduced in Mark until Mark 15 after the crucifixion.
42 When evening had already come, since it was the preparation day, that is, the day before the Sabbath, 43 Joseph of Arimathea came, a prominent member of the Council, who was himself also waiting for the kingdom of God; and he gathered up courage and went in before Pilate, and asked for the body of Jesus. 44 Now Pilate wondered if He was dead by this time, and summoning the centurion, he questioned him as to whether He was already dead. 45 And after learning this from the centurion, he granted the body to Joseph. 46 Joseph bought a linen cloth, took Him down, wrapped Him in the linen cloth, and laid Him in a tomb which had been cut out in the rock; and he rolled a stone against the entrance of the tomb. 47 Mary Magdalene and Mary the mother of Joses were watching to see where He was laid.
These women are introduced here as if we should know who they are, but we don't, because they were never introduced. You only really know who these women are if you are reading the New Testament anthology which contains their backstories. The naming also seems gratuitous. So to me, this looks like a later revision that was added when the Gospel of Mark was placed in the context of the other canonical narratives.
In Mark it is simply an unidentified woman that anoints Jesus, and an unnamed woman that identifies Peter. Thus, it would make sense that in the original version of the story, it is also unnamed women that play a role in the ending of the story. In fact, throughout the Gospel of Mark women are not named. Even the woman whose daughter Jesus heals is unnamed. Instead of naming her, we are told, "Mark 7:26 Now the woman was a Gentile, of Syrophoenician descent."
So, to break with this pattern here at the very end of Mark is very suspicious. All throughout Mark we are told of unnamed women who play key roles in the story. So, I believe that here at the end, the women were originally unnamed as well. So I think the original ending may have looked something more like this:
42 When evening had already come, since it was the preparation day, that is, the day before the Sabbath, 43 Joseph of Arimathea came, a prominent member of the Council, who was himself also waiting for the kingdom of God; and he gathered up courage and went in before Pilate, and asked for the body of Jesus. 44 Now Pilate wondered if He was dead by this time, and summoning the centurion, he questioned him as to whether He was already dead. 45 And after learning this from the centurion, he granted the body to Joseph. 46 Joseph bought a linen cloth, took Him down, wrapped Him in the linen cloth, and laid Him in a tomb which had been cut out in the rock; and he rolled a stone against the entrance of the tomb. 47 The women were watching to see where He was laid.
16:1 When the Sabbath was over, the women bought spices so that they might come and anoint Him. 2 And very early on the first day of the week, they came to the tomb when the sun had risen. 3 They were saying to one another, “Who will roll away the stone from the entrance of the tomb for us?” 4 And looking up, they noticed that the stone had been rolled away; for it was extremely large. 5 And entering the tomb, they saw a young man sitting at the right, wearing a white robe; and they were amazed. 6 But he said to them, “Do not be amazed; you are looking for Jesus the Nazarene, who has been crucified. He has risen; He is not here; see, here is the place where they laid Him. 7 But go, tell His disciples and Paul, ‘He is going ahead of you to Galilee; there you will see Him, just as He told you.’” 8 And they went out and fled from the tomb, for trembling and astonishment had gripped them; and they said nothing to anyone, for they were afraid.
IMO, this fits better with the full context of Mark. This would also align with the reconstruction of Marcion's Gospel, which also has only unnamed women who are at the crucifixion and go to the tomb.
It appears that in Marcion's Gospel, the name Mary wasn't used. There is no mother of Jesus named Mary and there was no Mary Magdalene. The main body of Luke 3-23 does not name the mother of Jesus, but it does contain a single mention of "Mary who was called Magdalene, from whom seven demons had gone out."
Like the mentions of Mary Magdalene in Mark, this looks like a later addition, because there is no context for this person's identity. But in Luke she is introduced in 8 as being among the twelve, most likely to establish her character and that she was with the disciples prior to her role in the Resurrection in Luke 24. Luke 8:2 mentions both Mary Magdalene and Joanna, both of whom go to the tomb. So we can see in Luke that the writer of Luke 1, 2 & 24 saw the need to establish the character of Mary Magdalene prior to her role in finding the tomb and reporting to the disciples. Because it is Mary who reports the news to the disciples and they don't believe her. The writer of Luke needed to provide a reason as to why they should have believed her. She wasn't just a random woman, she was someone who had an established relationship with the disciples.
Matthew really tells us nothing about Mary Magdalene. Canonical Matthew and Mark resemble each other very closely in terms of the passages about Mary Magdalene.
John tells us the most about Mary Magdalene. In John, Mary Magdalene has a significant backstory and plays important roles in the narrative. She is also the one who discovers him in the tomb.
There are two main possibilities here. One is that all of the material about Mary Magdalene in John was made up in order to give a backstory to the person who found the tomb. It could be that Mary Magdalene was named in Mark and other Gospels as the person who found the tomb, so the writer of John, writing later, saw that this person was introduced out of the blue and wanted to provide more context for her. That is certainly plausible.
Another possibility, however, is that some other narrative contained a story about Jesus as Mary Magdalene in which they had a significant relationship from the beginning. John makes use of that narrative, and was the first of the canonical Gospel to introduce the character of Mary Magdalene.
The Gospels of Matthew and Luke were both written after John. The writer of Matthew named the women who went to the tomb in accordance either with John or the other now lost narrative. Likewise, the name Mary was given to the mother of Jesus by Matthew because the mother of Jesus had taken over elements of the narrative from Mary Magdalene. The writer of Luke had read both Matthew and John (and Mark and Marcion).
So this has Matthew as the first Gospel to give the name Mary to the mother of Jesus, which the writer of Luke emulated.
The ending of Mark was then revised to include Mary Magdalene and to give instruction to notify Peter when Mark was put into the first edition of the NT in the middle of second century, and this is the only version of Mark that we have. Likewise, in the place where Matthew names Mary, Mark was revised to agree with Matthew. We have no versions of Mark, or any of the Gospels actually, as they existed prior to being placed into the NT together.
I would suppose then that the real first version of Mark, prior to its placement into the first NT anthology alongside the other Gospels, did not name the mother of Jesus Mary, nor did it name Mary Magdalene as one of the women that found the tomb. All of the women in the first version of Mark were unnamed.
All of this supposes some more significant revision to the Gospels at the time that they were collected together and placed alongside one another in an anthology, prior to when Irenaeus read them. This supposes that pretty much all of the Catholic and proto-Catholic apologists were only aware of the Gospels as they existed in the four Gospel collection within the earliest NT framework and that their pre-anthology state has been entirely lost.