Most of them are mixed up names or sound like nick-names. IDK whether some were official names and have since changed (eg did Drips O'Slimey change to Fang Bat or was that a nickname all along??) or if they're from fan art etc or spoilers (eg Chocostein's Monster)...I suggest looking into each one and trying to find where the reference was made. If the name isn't in the wiki then it probably does not exist under that name in game. Eg the cheetah piggle sounds like a nick name for the freckled piggle???
If it was one or two I'd look into it (as I have with the ones above) but a list of 87 is too extensive. Here is the wiki for all the pets in game. It should be helpful if you decide to research more pets or the ones from your list.
