It wasn't even the actual name of the character in Rocky; if I recall her name was Adrienne or Adriana and Rocky mispronounced it.
No, it's not a good name for a girl. (I happen to think it's not a good name for a boy either but that's neither here or there.) Adrienne and Adriana are perfectly good feminine versions of Adrian and there's no need to use Adrian.
We don't need to set the sky on fire. A little glow will do just fine.
Bob Ross