metadata.db is what makes it recognized as a 'Calibe Library' (folder)
The folder that contains this is the Library (and the name).
The name can be anything OS legal, but is best if you stay with basic ASCII characters.

I change the name from the default for my working Library (that is the one I back up)
The reason, if your Calibre configuration folder gets damaged, Calibre puts the defaults back and 'Calibre Library' will now show (without your books as that is not the Library you wanted)
Instant warning that something we WRONG and you should start your recovery plan.