Once a cat has been registered with TICA, you cannot change the name of the cat (unless there is a clerical error -- states it right on my TICA papers). The ownership paper has a transfer form on the back. You say you have the blue piece of paper. Once a cat has been registered (with that blue piece of paper), TICA keeps the blue paper and you get sent a registration of your cat.
Thus, your breeder may have registered the litter and then each individual cat needs to be registered and the breeder provided that blue form.
The breeders cattery always appears in the prefix -- that cannot be changed. You can select the pedigreed name for your kitty if those spaces are blank. They usually want an alternate name as no two cats can have the same prefix and name. The suffix is also for a cattery. Since you aren't not one, that will be left blank. That is used when a cat from a cattery has been used to breed to another cattery. My bengal's father is Gogees Spellbinder of Prince Royal -- He was a stud cat from Gogees and loaned to Prince Royal cattery.
The sire and dam for your cat should also be on the blue form. The breeders name will appear as well. Your breeder may have written in the sex, color, eye color, "not for breeding or showing", date of sale, etc.
The cost to register a cat was $12 and you can order a 3 or 5 generation pedigree for your cat for an additional fee. It is not required, but is interesting to see the cats in your baby's pedigree.
Hope this answers your questions. If not, we will try again.