In the book series, it depended on an apprentice's loyalty and readiness to take on the full responsibility for their clan as a Warrior. The leader will then determine if the apprentice is ready for the naming ceremony.
James Warrior's birth name is Will Warrior.
Sparrowpelt was Halftail’s warrior name before his tail was bitten by a badger(I think)
Bluestar's Warrior name was Bluefur.
Dovepaw's warrior name is Dovewing. Ivypaw's warrior name is Ivypool.
Rusty, or Firepaw's, warrior name is Fireheart.
Honeypaw's warrior name is Honeyfern.
Firekit's warrior name was Fireheart.
Bumblekit's warrior name is Bumblestripe.
The elvish name for warrior is "heru".
Featherpaw's warrior name is Feathertail and Stormpaw's warrior name is Stormfur
Leopardstar's warrior name was Leopardfur.
a she-cat or she-warrior.