Alignment is important, but the name of your god doesn't really matter. It's great color and all, but meaningless. See the other two answers for lovely tables of trivia.
You can see your current alignment in your status bar.
You can see the alignment of any altar.
A priest will match the alignment of the altar in his room. Unless of course you change the alignment of the altar, which will quickly lead to a drop in the altar room's population...
The name of the god associated with a co-aligned Altar/Priest is the name of your god.
Important: If you have not yet finished your Class Quest, changing your alignment can be very detrimental to your game...