Let's assume I have an .esp named "mod.esp". I have used that file in my game and my characters have content from it.
Now, if I renamed it to "file.esp" or any other name, without otherwise altering the mod, would all the content from prior the renaming be lost, or would the game recognize it as the same .esp? If yes, how would it behave on other people's games? If they had downloaded mod.esp, and now downloaded file.esp, applied to the game and deleted mod.esp. How would it behave? I'm assuming that in this case all the progress would be lost, but I'm not sure.

Seems I tried this once and it acted like it was a new mod.

Everything from the removed mod was gone, or undone. And I had to start from the beginning with the newly named mod.

Different names are treated as entirely different mods.

Yeah, think of what would happen if you changed the name of a master file, all the daughter?? mods would have a missing parent