Yet another operation that should be simple in ArcGIS Pro, but it's not. If you go to rename a feature class you are viewing in the catalog view, you face an issue. Upon a second click on the feature class (aka "soft click" or "slow click"), which normally enables renaming, the table preview reloads itself and renaming is disabled, returning you to the selection and table preview below.

Not an issue in ArcCatalog at all, which still does not have a Pro equivalent ( Offer a standalone ArcCatalog replacement for ArcG... - Esri Community ).