Not sure of the official 1st full "name that punky" game, but the first time Kyle does the impression on the show is the "voice" episode with Lake Bell. Check around the 32m 45sec mark of that ep. First actual 'name that punky' game has gotta be right around there.
In the episode "elections" they are all discussing southern slang like Tig's favorite 'tump'. Kyle keeps bringing up 'punky' as southern slang (from the context I think it punky=butt??). Pretty sure he slips up on the southern accent while saying 'punky' in that ep and throws a henry type accent on it, might have spawned from there.
