All Scriptures are quoted from the King James translation.
Four times in the Revelation Jesus uses that phrase(they are all in red letters):
Revelation 1:8 I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty.
Revelation 1:11 Saying, I am Alpha and Omega, the first and the last: and, What thou seest, write in a book, and send it unto the seven churches which are in Asia; unto Ephesus, and unto Smyrna, and unto Pergamos, and unto Thyatira, and unto Sardis, and unto Philadelphia, and unto Laodicea.
Revelation 21:6 And he said unto me, It is done. I am Alpha and Omega, the beginning and the end. I will give unto him that is athirst of the fountain of the water of life freely.
Revelation 22:13 I am Alpha and Omega, the beginning and the end, the first and the last.
But we know that Jesus was existent at Creation or before since:
Luke 10:18 And he said unto them, I beheld Satan as lightning fall from heaven.
It appears that Jesus had some other motive for using those particular words, rather than Eternal.