Is the Star Trek game franchise owned and operated under any one publisher? I know many developers have worked on games over the years, but if any of the games appeared on GOG, what publisher name would the games most likely be under?

The most recent game was published by Namco Bandai.

The rights are owned by CBS/Paramount, but they have licensed them out to several different publishers over the years; Activision, Atari, Interplay, Namco, etc.

Speaking of Star Trek games. Has there been a ST game where you control a Borg? Would be a cool game if you were a Borg that lost communication with the Hive on a Borg vessel. Other Borg of course trying to hunt you down and repair or disable you. Anyways, if it's not a game, there is a free idea for any game developers out there.

Unfortunately as of right now the Klingons and you know how they are.

There might've been a strategy game where you can play the Borg but I'm not sure on that. Also, I can see the Borg as playable in Star Trek Online eventually, but can't say for sure how that would be implemented.

It would be better to have a game focused on the Borg, instead of just added.

One idea would be to rewind the clock and show their original creation; you help the Borg in rising to power and becoming a galactic conqueror. That way it doesn't change the timeline, and if anything it fills in the gap as to how they were created and where in the Delta Quadrant they were originally. We're talking possible centuries of conquest and thousands of worlds to take over.

Star Trek: Armada (both of them) allowed you to play as the Borg Collective.

Not really what you are asking for, but there was "Star Trek: Borg", which was OK but not spectacular (the cardboard box was big and impressive though).

http://www.mobygames.com/game/star-trek-borg