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

That way, a game that lasts for several days/weeks will be difficult to follow. Using the sequential generation number is definitely better.

Well, the folder is already named after the initial generation (if you didn't realize it, the first 6 digits in the name represent the date:), i.e., the beginning of the game. I simply modified the current name by replacing the month number with a three-letter abbreviation – this makes it visually less jarring and added a hyphen between the date and the generation number.