HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

Well, there's no point in making the second player's name stick in hotseat mode. But when you play online, each player sets their nickname once on their own computer, and that's it. It's unlikely anyone would bother with it, just for a couple of players who play in hotseat mode, so that the name is saved. And if you need to look at the saves after the game, you can just enter a couple of random letters and see it.
And when starting a new game, the name of the PC owner (the first nickname) will always be there, and the second one can just be labeled as a "guest."