Well, Al-Anon has the "higher power" stuff, too, but all it really means is anything more powerful than you. Some people think of the power of the universe, or the power of the group.
And the "Hi, I'm ____" is just a tradition. It does help get to know people by name (anonymous groups aren't big on the name-tag thing, lol).
Try putting aside the things that annoy you. Try engaging in the "experience, strength and hope" part that is the heart of the program. I've never been to Co-Dependents Anonymous, so I couldn't compare, but I know I found a lot of relief in being surrounded by others dealing with the same kinds of craziness I had in my life. Try it for a little while. If you hate it, you don't have to go back. You still might learn some things, some tools, that will help you.