Preterists might identify him as Nero or some other first century person. Premillenialists are likely to say it is the leader of a reborn Roman empire, or perhaps the pope. Many of the Reformers agreed that it was the pope. That is because Christian tradition from the ealiest times associates this person with the idea of "antichrist." I'm talking about people like Irenaeus and Hippolytus. Those early Christians correlated scriptures like the Revelation beasts with Daniel's little horn and Pauline passages to identify an end time opponent of Christ. The church historian Eusebius said that those who followed the apostles were told that the one Jesus spoke of (John 5:43) was a lying, end time antichrist as spoken of in 2nd Thessalonians.
In the Bible we see the man of lawlessness called the "son of perdition." (2 Th 2:3) That is a title used only one other place in scripture, when talking about Judas (John 17:12). This lends credence to the idea that the man of lawlessness is a betrayer in the church. Note that when Paul speaks of the "temple of God"(2 Thess 2:4) elsewhere (1 Co 3:16-17, 1 Co 6:19, 2 Co 6:16) he is talking about the body of believers, the church.
Another first or second century writing that can be associated with this is the "Ascension of Isaiah."
2:4. And Manasseh turned aside his heart to serve Beliar; for the angel of lawlessness, who is the ruler of this world, is Beliar, whose name is Mantanbuchus. and he delighted in Jerusalem because of Manasseh, and he made him strong in apostatizing (Israel) and in the lawlessness which were spread abroad in Jerusalem.
AND now Hezekiah and Josab my son, these are the days of the completion of the world.
2. After it is consummated, Beliar the great ruler, the king of this world, will descend, who hath ruled it since it came into being; yea, he will descent from his firmament in the likeness of a man, a lawless king, the slayer of his mother: who himself (even) this king.
3. Will persecute the plant which the Twelve Apostles of the Beloved have planted. Of the Twelve one will be delivered into his hands.
4. This ruler in the form of that king will come and there will come and there will come with him all the powers of this world, and they will hearken unto him in all that he desires.
5. And at his word the sun will rise at night and he will make the moon to appear at the sixth hour.
6. And all that he hath desired he will do in the world: he will do and speak like the Beloved and he will say: "I am God and before me there has been none."
7. And all the people in the world will believe in him. 8. And they will sacrifice to him and they will serve him saying: "This is God and beside him there is no other."
9. And they greater number of those who shall have been associated together in order to receive the Beloved, he will turn aside after him.
10. And there will be the power of his miracles in every city and region.
11. And he will set up his image before him in every city.
12. And he shall bear sway three years and seven months and twenty-seven days.
13. And many believers and saints having seen Him for whom they were hoping, who was crucified, Jesus the Lord Christ, [after that I, Isaiah, had seen Him who was crucified and ascended] and those also who were believers in Him - of these few in those days will be left as His servants, while they flee from desert to desert, awaiting the coming of the Beloved.
14. And after (one thousand) three hundred and thirty-two days the Lord will come with his angels and with the armies of the holy ones from the seventh heaven with the glory of the seventh heaven, and He will drag Beliar into Gehenna and also his armies.
15. And He will give rest of the godly whom He shall find in the body in this world, [and the sun wil be ashamed]:
16. And to all who because of (their) faith in Him have execrated Beliar and his kings. But the saints will come with the Lord with their garments which are (now) stored up on high in the seventh heaven: with the Lord they will come, whose spirits are clothed, they will descend and be present in the world, and He will strengthen those, who have been found in the body, together with the saints, in the garments of the saints, and the Lord will minister to those who have kept watch in this world.
17. And afterwards they will turn themselves upward in their garments, and their body will be left in the world.
18. Then the voice of the Beloved will in wrath rebuke the things of heaven and the things of earth and the things of earth and the mountains and the hills and the cities and the desert and the forests and the angel of the sun and that of the moon, and all things wherein Beliar manifested himself and acted openly in this world, and there will be [a resurrection and] a judgment in their midst in those days, and the Beloved will cause fire to go forth from Him, and it will consume all the godless, and they will be as though they had not been created.
19. And the rest of the words of the vision is written in the vision of Babylon.
20. And the rest of the vision regarding the Lord, behold, it is written in three parables according to my words which are written in the book which I publicly prophesied.
21. And the descent of the Beloved into Sheol, behold, it is written in the section, where the Lord says: "Behold my Son will understand." And all these things, behold they are written [in the Psalms] in the parables of David, the son of Jesse, and in the Proverbs of Solomon his son, and in the words of Korah, and Ethan the Israelite, and in the words of Asaph, and in the rest of the Psalms also which the angel of the Spirit inspired.
22. (Namely) in those which have not the name written, and in the words of my father Amos, and of Hosea the prophet, and of Micah and Joel and Nahum and Jonah and Obadiah and Habakkuk and Haggai and Malachi, and in the words of Joseph the Just and in the words of Daniel.
Sometimes historians associate these passages with Nero who supposedly murdered his mother, but it appears to be taking about Judas (4:3) which has nothing to do with Nero. This could be a reference to Rev 17:16 if an apostate church is understood as a mother (Gal 4:26). The image, lawlessness, no other God, miracles, etc, remind us of 2nd Th 2.
More importantly the Ascension of Isaiah establishes a connection with the Belial/Beliar tradition, which means something like lawless or worthless one.
Deu 13:12 If thou shalt hear say in one of thy cities, which the LORD thy God hath given thee to dwell there, saying,
Deu 13:13 Certain men, the children of Belial, are gone out from among you, and have withdrawn the inhabitants of their city, saying, Let us go and serve other gods, which ye have not known;
Deu 13:14 Then shalt thou enquire, and make search, and ask diligently; and, behold, if it be truth, and the thing certain, that such abomination is wrought among you;
Deu 13:15 Thou shalt surely smite the inhabitants of that city with the edge of the sword, destroying it utterly, and all that is therein, and the cattle thereof, with the edge of the sword.
Deu 13:16 And thou shalt gather all the spoil of it into the midst of the street thereof, and shalt burn with fire the city, and all the spoil thereof every whit, for the LORD thy God: and it shall be an heap for ever; it shall not be built again.
Deu 13:17 And there shall cleave nought of the cursed thing to thine hand: that the LORD may turn from the fierceness of his anger, and shew thee mercy, and have compassion upon thee, and multiply thee, as he hath sworn unto thy fathers;
Deu 13:18 When thou shalt hearken to the voice of the LORD thy God, to keep all his commandments which I command thee this day, to do that which is right in the eyes of the LORD thy God.
2Co 6:15 And what concord hath Christ with Belial? or what part hath he that believeth with an infidel?
2Co 6:16 And what agreement hath the temple of God with idols? for ye are the temple of the living God; as God hath said, I will dwell in them, and walk in them; and I will be their God, and they shall be my people.