Registering a dog's name has no rules except for length. But there are some traditions.
1) Don't use a kennel name, unless you have permission to use it. (ex. my kennel name is Novel, if someone else used it I would be very upset, and the person that used it without permission would be ignored and/or ridiculed)
2) The registered name usually starts with a kennel name and then goes to the individual name, but it doesn't have to. If you don't have a kennel name, you can use your last name, or think up one. You don't have to register a kennel name, as nearly everyone abides by rule #1. Do a google search if you want to make sure you're not using someone else's name.
3) If either parent, sire or dam, was of record, the registered name of the get or offspring may tie into that popularity. (ex. Topper's registered name is Silhouette's Solid Gold, after his dad, Ch. Camelot's Go For the Gold.)
4) You can put their call name in there somewhere, if you choose, but it is not necessary. (Ex. I know a great dog named Ch. Nani's Indecent Exposure, his call name is "Streak". I love witty stuff like that.)