Maybe it's a regional thing, because I was told by several people that it's appropriate to have your sign name given to you by a deaf person and not to make it up yourself. I never went around asking for it, though, that to me seems rude. It should be something you want to do for a friend, I think.
I had a deaf friend who for some reason really loved my hair. So she gave me a sign name that mimics the shape of my hair.
There are a lot of rules in Deaf culture about the sign names of Deaf kids, but I don't know if they still apply or if it's only a deaf-of-deaf thing. Like the Supalla family have their own system of naming, I believe. There's actually a whole book about it but I can't remember the name at the moment.
I gave my fiancé his own sign name because he doesn't socialize with deaf people, but I needed a way to refer to him without fingerspelling his name over and over again. So that was just my convenience.
