Currently, auto-saved replays do indeed include a timestamp, which IIRC also precise to the second. I'm not sure if people may feel this creates an untidy replay folder if even applied to manually-saved replays.
At least with how I play, I would find the GUI always popping up to be very inconvenient. Timestamped replays would be more reasonable, as generally one would want to use the latest one; the only problem is, as mentioned, a messy folder containing lots of replays. These could of course be manually deleted.
Here's a proposal, which I would like some input on from other users:
Currently, there are two options in regards to replay file auto-naming: "On" or "Off". The default option is "On".
"On" automatically names the replay file after the level's rank name and level number in the case of a standalone level pack (including those made with the Flexi Toolkit) - eg Fun_01.lrb, or the level's name in the case of NeoCustLemmix or the editor's playtest mode - eg Just Dig!.lrb (it will automatically remove characters that cannot be in filenames, replacing them with underscores, and trim whitespace either side of the name). This . "Off" presents a Save File dialog any time the user attempts to save a replay. The default filename in such is the same as the automatic name when using "On", but this can be changed by the user. This option would remain as it currently is.
A second, seperate option could be added, which is whether or not to add a timestamp to the replay name. This would be added to automatic names when saving a replay, as well as to the default name when not using auto-naming. This setting (and the above one for that matter) would not affect auto-saved replays, which already have a timestamp anyway, and I think would be too much potential for data loss to apply this option to it (manually-saved replays, on the other hand, at least require some user input in order to erase anything).
The remaining question then is: What should the default options be? I would think that if the default option is auto-naming, it makes sense to have the timestamp turned on, because this way nothing will be lost - at worst, it will be hard to find. Those who prefer a tidier replay folder can change the option.
Another thing to consider: Should perhaps "Solved" or similar be added to auto-named titles, in cases where the replay offers a successful solution? Maybe this should be a seperate option?
Other proposals are welcome, of course, as well as comments on if/how this one should be changed.