The CK gives an error that says the mod name already exists, no option to update. I can't find an update button anywhere on the workshop page. How do you do it?

Edit: figured out why it was giving the error. Stupid thing throws a hissy fit if you modify the name of the esp at all. I had hopes for this workshop, but not impressed from the modder's side so far...

Wait, so let me get this straight...
If I change the name of the .esp file, AT ALL, my mod will no longer update and I'll need to make a new workshop file?

Oh, that is grade-A [censored] right there.

I am having the same problem too. Oh well, there's still the Nexus.

Nomenclature is key. With a different name, WS/CK sees it as a different mod. Not sure if there's a way to change the plugin's name, but you can change the mod name via the "Edit title and description" button on the Workshop. Whatever that name is, I'd imagine, will be what is displayed in a subscribers launcher regardless of the plugin name.

You could try renaming the .bsa, .bsl, and .ckm to match the desired plugin name and see if it still associates with the original upload?

Precisely that, yes.

Why would you possibly rename the ESP file? All that does is make it difficult for mod users, since Skyrim treats differently-named ESP files as completely different mods.

This, don't change Esp names, plan ahead.