Some ancient manuscripts of Peter’s second epistle have the Hebrew pronunciation, Simeon (συμεων – G4826), at 2Peter 1:1, while others have the Greek pronunciation, Simon (σιμων – G4613). Apparently, a later copyist changed Peter’s given name at 2Peter 1:1 to what he thought it should be. Throughout the Gospel narratives Peter’s given name is recorded as Simon, or the Greek pronunciation of his name. Probably, the copyist originally changed what Peter wrote at 2Peter 1:1 from συμεων (G4826) to σιμων (G4613), rather than the other way around. I can see no logical reason anyone would change how Peter’s name is written in the Gospels to agree with how his name is written at Acts 15:14, which is the only other place in the New Testament where Peter’s given name is written according to its Hebrew pronunciation.
Nevertheless, no matter which pronunciation we use, Peter’s second epistle is the only book in the New Testament whose author identifies himself with two names. Moreover, since the name Peter obviously would point to the apostle, because he is the only person in the New Testament addressed by that name, it seems rather redundant to add his given name unless there is a hidden reason for doing so. Therefore, it may be a very significant matter, considering Peter’s letter was written during a time of persecution, and some things that need saying in such times must be done under the guise of secrecy. After all, if the enemy was often present with the believers during worship services (cf. 2Peter 2:10-15), it wouldn’t be wise to let him in on every detail of the works of the church leaders.
Therefore, it may be wise to consider some words that Peter wrote in this epistle (like his double identity) may have a deeper meaning, pointing to something written elsewhere in Scripture. For example, Peter is referred to in the Synoptic Gospels specifically as Simon Peter only at Matthew 16:16 and Luke 5:8. Peter could be pointing to one or both of these Scriptures. On the other hand, if Simeon, the Hebrew pronunciation of his name, is the correct rendering at 2Peter 1:1, Peter may wish to point to Acts 15:14 and what was said or done at the Jerusalem Council. At that point James, the brother of Jesus, referred to Peter by his Hebrew name. Peter might be referring to what he said at the council or perhaps, and more likely, to what James said.
Assuming some of Peter’s epistle was written so only believers would understand what Peter means to say, and if Simon is the correct pronunciation of the name he used, then Peter may be reminding folks in Asia Minor that Jesus is the Messiah, the Son of the Living God (Matthew 16:16), and / or they need to repent and hold Jesus in awe (Luke 5:8). Nevertheless, Peter often refers to Jesus as the Christ or Messiah and calls for repentance in very clear terms (2Peter 3:9), so, as I said above, I don’t believe Simon is the correct rendering here.
More likely the Hebrew pronunciation, Simeon, was originally written by Peter. He may have been using it to point to a specific timeline in church history when the subject of circumcision was an issue among believers, which might also apply in some way to the present persecution in Asia Minor. In Acts 15:7-11 Peter claimed that God placed no difference between Jew and gentile, in that the hearts of the gentiles are purified by like faith (Acts 15:9, 11; cf. 2Peter 1:1 “like precious faith”). However, since only James is recorded as using the Hebrew pronunciation of Peter’s name (Acts 15:14), Peter could be pointing to what James wrote in what is called the Apostolic Decrees (Acts 16:4), or to specific things in James’ later epistle. If James was slain at Jerusalem for writing his own epistle to the Diaspora, it would behoove Peter not to refer to this epistle directly, but in code. By pointing to the only other person in the New Testament to use Peter’s Hebrew name, Peter may be reminding the believers to reread what James had recently written to all the churches of the Diaspora (James 1:1).
We know that the persecution Peter mentions in his letters couldn’t be the persecution begun by Nero in 64 AD (cf. 2Peter 2:1-3; 3:14-16), because Rome didn’t combat threats with false or counter teaching. They simply removed the threat by force. The persecution Peter mentions in his epistles wasn’t intended to be a bloody persecution. Therefore, it could not have been directed by Rome. However, there are several things that Peter might want to remind his readers that James mentioned. For example, James mentioned that the whole of the Diaspora was engulfed in a severe trial (James 1:1-2; cf. 1Peter 1:1, 6). Secondly, the days of the power of those who are rich in themselves (viz. the authority behind the persecution at Jerusalem) are coming to an end (James 1:10-11; cf. 1Peter 1:6), but he who endures to the end of the trial will be acknowledged by Christ (James 1:12; cf. 1Peter 5:4). Thirdly, James had addressed issues of oppression (James 2:6) and respect of persons (James 2:1, 9) or believing that riches were the blessing of great faith and poverty was the discipline of weak faith (James 2:14-16). Finally, James 3:5-6,10 may be an allusion to the mouth given the Beast in Revelation 13, and, if so, James’ tongue / mouth would be Annas, the high priest, who set ablaze the trial the believers were then experiencing. A little allusion by Peter in his epistle could go a long way in helping the brethren understand what was going on, and encourage them to keep enduring until the end of the trial.
 In the Gospel of John Peter is always referred to as Simon Peter, so a distinction is evident only in the Synoptic Gospels.