I have a litter of Maine Coon kittens who will be leaving soon with their adoptive families. With each little bundle of fur being placed in a carrier on the way to its new home, I ask the excited parents, "Have you thought of a name for him or her yet?"
I give each litter born in my house a theme and the kittens are given call names accordingly. We've had the traditional Disney theme (Mickey, Minnie, Donald) and contemporary Disney (Mulan, Jasmine, Aladdin); book characters (Atticus, Edward, Bella); music (Do, Re, Mi, Fa, So, La, Ti); Rock bands (Santana, Nirvana, Bob Marley, Pink Floyd); Greek (Aphrodite, Persephone, Hera), the four seasons, etc. It's fun, gives me something to call them for the 12 weeks I have them and helps me to keep track of which litter a cat came from. Most of my kitten buyers will come up with their own name for their kitten which is the one I'll send in for the registration papers.
The cat registry associations (I use CFA and TICA) have a rule that each cat name registered has to be a unique name. The first part of every pedigreed cat's name is its cattery name (the feline equivalent of a kennel). My registered cattery is called Dracoonfly, therefore, all kittens I register start with Dracoonfly. There can be more than one registered cat named Oliver, but only one Dracoonfly Oliver. Another cattery would have their name in front, i.e. Broadsway Oliver where Broadsway is the cattery name. Thus, the two names are technically different.
If I get a kitten from another breeder, it will have the cattery name it was born under as the first part of its name and I can designate my ownership by tacking my cattery name on after the given name and the word "of", i.e. Broadsway Cascapedia of Dracoonfly. Cascapedia or "Cassie" was born at the Broadsway cattery and is owned by the Dracoonfly cattery.
If a new kitten owner wants to call their kitten a name that's already been taken by one of my clients, I just ask them to add a second name or change the spelling. There is now a Dracoonfly Oliver and a Dracoonfly Oliver Elvis, a Dracoonfly Phoebe and a Dracoonfly Feebie.
I name all the cats I keep after fishing flies. The cat often has a different call name, for instance Dracoonfly Miramichi Special goes by "Myra". The Miramichi Special is a fishing fly. There are also fishing flies unsuitable for cat names that I avoid, such as Moose Turd, Mouserat, or any of the leech names.
There are an infinite number of sites dedicated to cat names on the web for those seeking that perfect name. I found Catster's top 100 female and male cat names, sent in by their followers. Topping the list for female names is Chloe; for males, it's Tigger.
Although most people can't tell if the name they pick is one the cat likes also, choose your kitten or cat's name carefully and make it as special as your pet.