I have always wanted to make a list of "special" names my clients and myself come up with for various exercises...
for example...the first time I had a particular client do band "swims" (as JC Santana calls 'em)...my client dubbed them the "prison shuffle" b/c of the bending over at the waist action, lol!
same client has also designated plyo pushups performed with hands landing in alternating fashion on med ball at top of movement, then ground at bottom, "el diablo"...

i have some crazy clients!
i like having my own names for exercises that need 'em...both nothing too far-fetched!
i would say leave the old files for the new trainer...if they are fairly savvy, they should "get" most of it...i'm a big believer in files anyway...they are a great resource!