Saying, I am - The Christ, is added by eight MSS., Coptic, Armenian, Saxon, and four of the Itala.

For many shall come in my name,.... Taking upon them the name of the Messiah: saying,
I am Christ; the word "Christ", is rightly supplied from Matthew 24:5; otherwise in the original it is only, "I am"; which the Persic version doubles, reading it, "I am indeed, I am": he that was promised and expected, the true Messiah; he that was to come:
and shall deceive many; See Gill on Matthew 24:5.

For many shall come in my name, saying, I am Christ--(see Matthew 24:5) --"and the time draweth nigh" (Luke 21:8); that is, the time of the kingdom in its full splendor.
and shall deceive many--"Go ye not therefore after them" (Luke 21:8). The reference here seems not to be to pretended Messiahs, deceiving those who rejected the claims of Jesus, of whom indeed there were plenty--for our Lord is addressing His own genuine disciples--but to persons pretending to be Jesus Himself, returned in glory to take possession of His kingdom. This gives peculiar force to the words, "Go ye not therefore after them."