Names for the clans are incredibly important, not only showing you traits, but also your social standing and status
Names are structured thusly:
Family name -> prefix -> prefix-paw -> prefix-suffix
The exception to these rules is Honor titles or Dishonor titles, one being given for a great accomplishment, the other for a great crime.
Family Names are what a kitten is named before they reach 3 moons. it's usually two words, describing the kitten's general appearance or temperament. These name's are endearing, short and cute, to show the love the parents have for the kit, something like "sweet flower", "big stretch", or "fluffy flick". Only the Immediate family should use the name unless given permission, and kits gain their prefix at 3 moons.
Prefixes are based on a kittens personality, appearance or circumstances. Most names are given by the leader, with input from the parents. These names/prefixes can change before apprenticeship due to circumstance or a shift in personality.
Paw is the suffix after the prefix when you are currently still in training.
Suffixes indicate many parts of you, if you're fully trained, your personality, your skills, stuff like that.