Basically, Hime, you choose the first part of the cat's name, if it's in newborn, kitten, or adolescent form. However, once it reaches adult form, the last part of it's name will be able to change to whatever you like it to be. ^^
For newborns and kittens, the last part of their name will always be 'kit'.
Example: Starkit, Brownkit, Frecklekit, Springkit, etc.
For adolescent's, the last part of their name will be changed, but you won't be able to pick what it is quite yet. However, as adolescent's, the last part of their name will always be 'paw'.
Example: Starpaw, Brownpaw, Frecklepaw, Springpaw, etc.
For adults, as these cats have matured and gained their warrior name, usually, the last part of their name is changeable to anything you'd like.
Example: Starpelt, Browntail, Freckleface, Springfur, etc.
If you're wanting to look at examples and all, the Owner's List is on the 2nd page. Keep in mind though, unless you have an adult kitty, you can only choose the first part of the name for right now, until they've earned their warrior name. ^^