http://www.angelfire.com/empire/serpentis666/Baptism.html
This is Satanic Baptism. But this is something you would do for your newborn child, if you have one and if you are able to raise them in exclusively Satanic ways. This would most likely be when you have a partner who is also a Satanist, or when you are raising your child on your own.
Like Νίκος said, there is no need to do this for yourself, as you are already of Satan once you do the dedication ritual.
As for names, you obviously keep your name too, of course. There is no name changing when you dedicate. Unless this is your choice and you legally do it.
But if your question is regarding how to name a newborn child, there is no rule for this either, but if you want to name your child in a Satanic fashion, I'd say you could try to come up with a unique name. By unique, I mean a name only your child answers to, and no one else. Not like "John", "Mary", "Paul", etc. Such common names kind of defeat the purpose of a name in the first place, which is to identify an individual. The Gods mostly have genuinely unique names (despite some things like bands being named after them), so to me, coming up with a unique and original name is the best line of thought when naming your child/pet. I named my last cat "Petrusko" (which someone suggested to me). Perhaps your GD can assist you with that choice, too. But again, there are really no rules for this.