There is addressed in the FAQ: http://www.thetournamentdirector.net/faq.html#faq18
Basically, it's a painful situation, no doubt about it. I'd like to address it in the software, and I'm pretty sure I can, but it isn't terribly high on the priority list (hasn't happened too much). The fix would be to allow you to "merge" DB players, but basically it boils down to "now you have two players who are the same player", and the software would have to keep track of that. Do it again and you now have 3 players who are really the same player. And so on. Could slow the software down, and I'm trying to avoid that.
I'm not certain what was meant by "at some point the software stopped checking for names...", because the software does check for duplicate names. At 2.1, the software stopped DISallowing duplicate names, but it will still warn you if you add a player with the same nickname or the same first + last name combination.
So, if you have two players A and B in your database who are actually the same player, you have to change player B to player A in all of the tournaments in which you have player B instead of player A. Or vice-versa.
Delete player B in the database. Load each saved tournament. Player B should now show up as "not in your database". Edit the player and use the Merge function to merge the player with database player A. Save the tournament. Wash, rinse, repeat.