Some users may like/need to code offline, run a few tests when they come back online, and repeat.
Do you mean that it would require too much storage? Then maybe the different names could be saved locally by the plugin? Even for a user who has done hundreds of puzzles, that shouldn't be too heavy, and clearing local data occasionally would keep only the puzzles last tried. Another solution would be to use a file named after the puzzle (ex: title of the puzzle in camel case), so that there would be no need for extra memory.
Anyway there is no work-around the argument "i don't have enough time to do it", what you did is already great, thanks!