Why Bar Jonah?

[Giuseppe]

I am interested in this since I read this post on Vridar.

Why Simon Bar-Jonah?
Not even Robert Gundry says something in his fascinating book on the Peter of Matthew.

If it is a reference to the prophet Jonah who lived in the whale, then Peter would be an apostate like Jonah. But Jonah repented. So even Peter repented? And if he repented, then Peter would not be an apostate in Matthew, against the Gundry's thesis?

Can there be some link with :

Matthew 12:38-39
Then some of the Pharisees and teachers of the law said to him, “Teacher, we want to see a sign from you.”
He answered, “A wicked and adulterous generation asks for a sign! But none will be given it except the sign of the prophet Jonah.


''the sign of the prophet Jonah'' may be the same son ''of Jonah'', that is Peter? In that case, Jesus is saying that Peter will be a ''sign'' for the Pharisees and teachers of the law? An cipher for them?