I've always used "finals" and understand it to be an abbreviation of "final checks". A similar usage as academic "final exams" - "finals" at university. Pilots made the necessary final checks in order to be able to land (or go-around) safely, and probably used the word to themselves as a prompt (as in the more modern "red, blue, three greens" - or "four" greens if it's a Harrier) before the use of radio. When RT came along, that point in the circuit just got named after the actions the pilot was performing at that time.
That's my understanding of it - and that's final!
