I have to agree with the other posters.
Those names don't show up on any Goju (or Uechi, or Ruei-ryu, or Shorin style for that matter) kata list.
Possible that they are different names for "standard" kata but if so I would want to know why the "other" names are being used.
If I was a student there.
BTW as already has been mentioned, the translations you post may MAY actually refer back to a specifc kata.
Gekishi "could" be translated as "demolish or destroy" MAYBE.
Shotokan has a couple of kata that "MAYBE" you could work into a somthing like "ten human" (well "ten" anyway)
Goju's Sanchin can mean "three battles" so its got the "three" in the "Togather Three" thing.
As the story goes Goju, Uechi, and the rest of the "Naha" systems pretty much focus on techniques from the Tiger, Crane and Dragon systems.
So maybe MAYBE the "Way of Three Animals" things refers back to that story.
Gotta tell you though, this sounds pretty weird to me.
As a VERY general rule I always do a "double take" when folks start pulling out non-standard terms for what they do.
Sure there is going to be regional differences in terms--but that is EXACTLY why most trades/hobbies etc have specifc terms for what they involve.
I ask a mechanic or carpenter for an Phillips Head screwdriver--don't care where in the States he is from, he better know what I am asking for.
I ask a plumber to hand me his "snake" I better get a drain cleaning tool
I ask a someone I am climbing with to hand me a "biner" and they had better know what I am asking for.
Weird, unusual, non-standard, terms that don't appear anywhere else in context with the hobby/profession etc that you are doing could very well be a red flag.
Just somthing to consider.