Just make sure Lightroom isn’t running when you mess with the catalog!
Very true! It’s fine to rename the catalog. Just shut down Lightroom before doing so AND be sure to rename the Previews folder accordingly. (There should be no “.lrcat.lock” or “lrcat-journal” files present when you rename the catalog.)
For example, if your previous Lightroom catalog was called “Jimmys Photos”, then the Previews folder would be called “Jimmys Photos Previews.lrdata”, and if you wanted to rename the catalog to “Jimmys Portfolio”, then you would also want to rename the Previews folder to “Jimmys Portfolio Previews.lrdatea”.