The cat naming conventions in the WB universe are slightly different from those of the Warrior Cats series.
Kits use the suffix -kit, as per normal, just as apprentices use the suffix -paw.
Warrior suffixes are where things here differ. Instead of -paw turning into a suffix of the leader's choosing, their suffix will become that of one of their parent's (usually the mother's, though this differs from mate to mate). Think of it as a sort of surname.
For example, a apprentice named Dawnpaw's mother was named Pebblelight. This would mean that Dawnpaw's warrior name would be Dawnlight, and she would pass this suffix down to her own kits. If it is the leader's kits, their warrior suffix will be the same as the leader's when they were a warrior, NOT -star.
The reason behind these naming conventions are because a main theme of WB is family and their legacies and bloodlines, hence the name. Having these names be passed down is almost like a 'passing of the torch,' not unlike how we Twolegs pass down our surnames through our families.