No, not those type of parents who want to call their offspring Apple or La-a, but rather from the 'every player who played' list which I've been updating. This is the list of players who don't share their first name with anyone else; nor their last name with anyone else. I've tried at best to find their birth name to make this authentic, but there will be some who will probably be taken out because it's a nickname or a shortened form - eg. Gil Butchart or Jez McLennan. Anyway here is the list, with debut year if there is no DOB:
A-J: