User blog comment:Kogath/Monster Hunter 4 Ultimate for the Nintendo 3DS/@comment-21371438-20140219154401/@comment-184612-20140219200148

The only one you get to customize is your Leader Felyne. The rest of them you either get through finding them on hunts (typically in the Felyne camps or randomly in the Unknown Forest), DLC, or from other Hunters.

For the Leader you can change Ear Type, Eye Shape, Fur Pattern, and of course colors as well as the Voice Type (most of them are really... Odd). The Felynes you find out in hunts will have random types and looks. You can name them when you get them or go with a default name, but there's no option to rename them later.