Got a name, got a game.. No findings in USPTO.. but-

Well you can't patent a game for one thing. So your worry seems slightly redundant.

IANAL but... you can patent mechanics used within a game if you can make a convincing case for their innovative use by you - but that doesn't necessarily mean that the mechanic is unique to that game.
(Patenting a specific board design might be a different case in terms of reuse but it seems to me that trademark law might be better grounds for protection than a patent.)

And the patent would thus protect the specific implementation of that mechanic as proposed by you. So I suspect that changing that mechanic would mean that the new version would not be protected, although I also suspect that you could probably argue a case that would cover it. But I doubt this would be worth the hassle...

This isn't a terrible helpful answer I realise :)

Copyright is an even murkier area than Patents, simply because of the adage "there are no copyrights in ideas".
And copyright applies effectively automatically (i.e. you don't need to apply for it, or anything like that.)

But basically the parts of your design that are covered by copyright are the parts that people could not reproduce without others knowing where the parts had come from.

So, for instance, you can make a trivia game with a roll-and-move board and various categories of questions - not breaking copyright.
But if you have a round board with coloured spaces, spokes going to the centre and "roll again" spots then you are going to get into trouble :)

Likewise, the rules of a game are not covered by copyright, but the particular version that is published and comes with the game is. This allows people like Tom to write reviews that can give a pretty detailed outline of how a game works without infringing copyright.

This means that you can change aspects of your game as much as you like and it will still be protected by copyright. The only real difficulty is that copyright protection just isn't worth that much! Even if you created the next Cranium, no-one is going to try and steal the idea, and even if they did it just wouldn't be worth their while (nor, probably, yours to fight it.)

Basically, what I'm saying is that you shouldn't worry about stuff like that until almost the end of the process, if at all. If you're sending a prototype off to a company then having a recorded date is useful, for instance, but really not that significant.

(There's also trademark protection, but that only really applies to things like the name of the game and/or jargon terms, and is even less worth worrying about!)

Probably an even less useful answer than the first one ;) ISTM that first-time designers get more bothered about issues like copyright and the like than "old hands" (even if those old hands haven't had anything published themselves!) simply because you feel that the investment you have made in time, energy and money should have some protection. Whereas sadly, the truth is that, just like most creative artists (writers, composers, painters etc.), all that effort is only really going towards beginning to produce a solid foundation for future work rather than being a stunning blockbuster success that the whole world talks about... (hence the famous joke about becoming an overnight success after twenty years.)

In the field of graphic design I would imagine that people "borrow" ideas all the time, which makes protection more of an issue.
The thing is though that you still can't protect the "idea" - only the execution of that idea.
I can however see why a duck in a sailor suit would be considered to be plagiarism even if there are no other similarities ;)

Whereas board games are largely made up of existing ideas (mechanics) that are chained together in new ways (and even then, the new ways aren't always as new as all that!) Sometimes a game uses the old idea in a startlingly new way, which can mean that no-one else can even try to attempt it without making the origin really obvious. But in general, everything is always up for grabs: what you have to do is to make your version sufficiently interesting that people will want to play it in preference to another game that may use similar ideas.

As to when a game is "finished", the answer is never :) It took Dirk Henn three goes (and that's just counting the published editions!) to get to "Alhambra", and even that may not be the end of the line. Games are like books or artwork to some extent, in that they are never truly "finished". The difference with games is that they can be continually revisited (through variants, rule changes and radical revamps) which makes them interesting.