CC maintains one library. You can "sync" with as many calibre libraries as you want, but the books will be combined into the one CC library. If you want to be able to distinguish between calibre libraries in CC then you need metadata that permits that, for example a custom column containing the library name. It is a very similar to the process for distinguishing between virtual libraries as
described in this FAQ, except that the value is filled in manually or using the current_library_name template function in a "column built from other columns".