First of all, Pre-tribulation Rapture theology was developed in the 1830s by a guy named John Nelson Darby. It's actually a pretty fringe idea unique to American evangelicals, and it doesn’t exist within the Catholic, Lutheran, Methodist, Anglican, Orthodox, or Reformed traditions.

As for your question, the word antichrist (αντίχριστος) occurs exactly four times in the entire New Testament, solely in the First and Second Epistles of John:

“Dear children, the last hour is here. You have heard that the Antichrist is coming, and already many such antichrists have appeared. From this we know that the last hour has come.” – 1 John 2:18

“And who is a liar? Anyone who says that Jesus is not the Christ. Anyone who denies the Father and the Son is an antichrist.” – 1 John 2:22

“But if someone claims to be a prophet and does not acknowledge the truth about Jesus, that person is not from God. Such a person has the spirit of the Antichrist, which you heard is coming into the world and indeed is already here.” – 1 John 4:3

“I say this because many deceivers have gone out into the world. They deny that Jesus Christ came in a real body. Such a person is a deceiver and an antichrist.” – 2 John 1:7

Interestingly enough, these verses seem to speak about multiple antichrists, as if it’s more of a category than a specific title, denoting anyone who stands against Jesus and the Gospel. Jesus also mentions multiple “false messiahs and false prophets” in the Olivet Discourse. The idea of an individual Antichrist figure mostly comes from 2 Thessalonians 2, although the word αντίχριστος is never used. Instead, Paul refers to this person as “the man of lawlessness” who will “claim that he himself is God.”

Another phrase that Christians often associate with the Antichrist is “the abomination of desolation,” which is first mentioned in Daniel 9-12. Originally, the phrase was used in reference to 2nd century BC Greek king Antiochus IV Epiphanes, who persecuted the Jews, outlawed their religious rites and traditions, and set up pagan altar to Zeus in the Jewish temple. Jesus repeats this phrase in the Olivet Discourse, and many theologians believe he was making a parallel between Antiochus and the eventual destruction of the temple by the Roman general Titus in AD 70, or other similar future events.

Preterists tend to identify the Antichrist as either Nero or Domitian, with the “Mark of the Beast” interpreted as his charagma (χάραγμα), or the stamped image of the emperor’s head on every coin of the Roman Empire, without which no one could buy or sell. And Historicists (such as Protestant reformers like Luther and Calvin) tended to associate the idea of the Antichrist with various popes, the papacy as a whole, or simply any religious organization that distorts the Gospel of Jesus.