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You can move or rename the catalog in Explorer (Windows) / Finder (Mac) as if you were moving or renaming any other file, but don’t forget to close Lightroom first.
Ideally you should also move or rename the previews folder (Windows) / file (Mac) so that it reflects the new name of the catalog too. If you don’t rename the previews correctly, Lightroom will simply recreate all of the previews. No harm done except for the time involved, although if you have offline files, previews for those photos won’t be recreated until they’re next online. If Lightroom creates previews with a new name, you may want to delete the old previews file to regain the drive space.
So, for example:
Lightroom Catalog.lrcat —> New Name.lrcat
Lightroom Catalog Previews.lrdata —> New Name Previews.lrdata
When you next come to reopen Lightroom, hold down Ctrl (Windows) / Opt (Mac) to navigate to the renamed catalog, or just double-click on the catalog file. You may need to change the default catalog (in Catalog Settings) so it opens the correct catalog automatically in future.