Puppy is really easy to remaster to incorporate your won changes. Quite a few folk in the Puppy community make available their remastering efforts. At last count there were over a dozen variants of Puppy out there. The variants are all unofficial and not supported by Barry but you can ask about them on the forums.
Naming wise, "bone" is obviously a joke to do with "puppy", and barebones is a reduced minimal puppy, as is meanpuppy and litepup, while onebone is puppy with console only apps. There are too many others to mention, since the included remaster script makes it a simple matter to roll your own pup in a half hour or so.