Prefixes are the beginning of the name, whereas suffixes are the end of the name. For example, a prefix for a warrior could be Harvey, then the suffix would be flame. Creating their warrior name; Harveyflame.
Kittypets can have almost any name they want, as long as it isn't innapropriate. When someone becomes a kittypet, they must choose a kittypet name, and are not allowed to keep their Clan name.
When someone becomes a Loner, or a Rogue, they must keep the Clan name they had/have, meaning if they have an apprentice's name, they're stuck like that forever.