Omega is the name of a cat I had once. She was a tabby, and the markings on her head looked like an "O", so I wanted to find a name for her that began with "O". Her name actually just got shortened to Meg after a while.
Also, Omega is the last letter of the Greek alphabet. You see the letter "omega" in a lot of church paintings and carvings because Jesus said "I am the alpha and the omega. The beginning and the end." I toyed with whether to call myself Alpha or Omega because I couldn't decide whether I was ending something or beginning something. In the end I went with Omega as at the time I was feeling more like I was ending something.