It's a strange terminology. I don't think there is a Jewish equivalent of 'antichrist' in terms of its construction. The messiah is simply 'the one anointed.' The whole concept of anti-Christ makes no sense in Hebrew. It makes little sense from any Greek sources before Christianity. The only way it makes sense is if the Marcionites posed 'another Christ' who was against the Law and prophets and so was in effect 'the Christ of the Antitheses' = the Antichrist. The first reference to 'Antichrist' in Against Marcion:
But antichrist cannot be utterly overthrown unless we make room for the refutation of the rest of his submissions, by relaxing our argument from prescription (not to combat unrepentant heretics). Let us then at this point consider, in terms of his Christ, the actual person, or rather the shadow and phantom, of that god,2 and let us make an evaluation of him in terms of that for which he is thought an improvement on the Creator. Now there have to be definite rules for evaluating the goodness of a god: though I shall first need to find and lay hold upon that goodness, for then only can I adjust it to the rules. (1.22)
Let the heretic now give up borrowing poison from the Jew,— the asp, as they say, from the viper: let him from now on belch forth the slime of his own particular devices, as he maintains that Christ was a phantasm: except that this opinion too will have had other inventors, those so to speak premature and abortive Marcionites whom the apostle John pronounced antichrists, who denied that Christ was come in the flesh, yet not with the intention of setting up the law of a second god—else for this too they would have been censured <by the apostle>—but because they had assumed it incredible that God <should take to him human> flesh. So Marcion, even more of an antichrist, seized upon this assumption, being better equipped in fact for denial of Christ's corporal substance, in that he had postulated that even Christ's god was neither the creator of flesh nor would raise it to life again—in this too supremely good, and entirely divergent from the lies and deceptions of the Creator. And that is why his Christ, so as not to tell lies, or to deceive, and in this fashion perhaps be accounted as belonging to the Creator, was not that which he appeared to be, and told lies about what he was—being flesh and not flesh, man and not man, and in consequence a Christ <who was> god and not god. (3.8)
Now who is that man of sin, that son of perdition, who must needs be first revealed before the Lord's coming,—he who exalteth himself above all that is called God and all that is worshipped, who will take his seat in the temple of God and boast that he is god? We affirm that he is antichrist,
as both the old and the new prophecies explain, as does John the apostle who says that antichrists have already come forth into the world,b forerunners of the spirit of antichrist, denying that Christ has come in the flesh, and dissolving Jesusc—meaning in God the Creator: though I suspect that according to Marcion antichrist is the Creator's Christ, for in his view <that Christ> has not yet come. But whichever of the two he is, I should like to know why his coming is with all power and signs and lying wonders. Because, he answers, they have not received the love of the truth, that they might be saved, and for this cause it will become for them an impulse of delusion, that they all may come under judgement who have not believed the truth but have taken pleasure in unrighteousness. So then if this is antichrist, and he is imitating the Creator, it will be God the Creator who sends him to thrust down into error those who have not believed the truth, that they might be saved: and the truth and the salvation also will belong to him who takes vengeance on their behalf by the substitution of error, that is, the Creator and to him also belongs that jealousy in deceiving by error those whom he has not gained by the truth. If however it is not antichrist, as we suggest, then it is the Creator's Christ, as Marcion claims. But how can it be that <Marcion's god> should send the Creator's Christ to avenge his own truth? But if he agrees regarding antichrist, I go on to ask how it is that <Marcion's god> should have need of Satan, the Creator's angel, and that <Satan> should be slain by him, when his task is to put
in operation the working of delusion on the Creator's behalf. (5.16)
Tertullian's point is that to argue that the other Christ aside from the one predicted in the Law and Prophets is the Antichrist. But the argument that there is another Christ besides the Christ of the Law depends on the Antitheses.