How do cats get their names in Warriors?

A kit is usually named by what a cat sees and encounters in its life. (by werewolf96... I think you got mixed up with The Tribe of Rushing Water there. The Clans do not do that the name's are just up to the Queens) The kits are usually named by their mother. If a kit was named leaf then the kit would be called Leafkit. An apprentice would be Leafpaw and a clan leader Leafstar. When an apprentice is finished with his/her training he/she can become a warrior. The first part of the name stays the same but the second part changes from "paw" to something in nature/in a cats life. The clan leader decides the second half of the name and they try to make the name make sense. This will be the permanent name unless the cat becomes clan leader. It is also possible, in rare circumstances, for a clan leader to change the first half of a cat's name, or to change a cat's name altogether. This can be seen in warriors book 6, when Firestar renames Lostface to Brightheart. (Or in Bluestar's Prophecy-NO SPOILERS- Sparrowpelt to Halftail)

Or if you mean how does Erin come up with the names that would be basically they write them out on a piece of paper (say on one side snow, rain, fire, soot...etc) then on the other side the second half of the names (say fur, whisker, heart, fur...) something like that.--werewolf96