Why don't we just stick with Macky's numbers, which I believe are the same as Jessica's, for official designations. Conversationally, I wouldn't mind picking up some names, but I'd prefer to see numbers in forum posts.
Bob has good names for groups, but it has always irked me that he renumbered them from Macky/Fridrich.
I do like some of Jason Thong's terminology for things like "joined set" and "potential set", but his OLLs rename things that already have accepted and widespread common nomenclature. The 7 edges oriented OLLs, in particular, have common names: U, T, Triple-Sune (L), Sune, Anti-Sune, Pi (Bruno) and Double-Sune (H). Build from there.