Re nameing tools and/or "making them one's own" how does everyone feel about "blooding" their tools or marking them with blood, oathing to the spirit (within the tool or to that with which one works). Obviously a tool so marked could never leave one's possession, but I have marked (some of) my tools with many things from my body.
It's a valid method of bestowing personal essence and power to an item. It's not for everyone, and not used on everything, but binds a special item a little more closely to you.
On the original subject, I'm going to agree with Magentarose. A name is just a word. To call a cat a feline or a dog a canine doesn't change what they are. I see no value or use for a witch-name but no harm either. It's a matter of personal taste. If you really feel the need to have one, choose one, but I suspect that you'll tire of it.