After you select an instance to rename (wildcards such as * work to select multiple instances) and have entered in the new name, you have two options. Clicking “rename to” applies the change to the selected objects and leaves the dialog box open for more selections. Clicking “OK” applies the change and exits the command. (I’m not sure why they didn’t just have an “apply” button like most other dialogs of this nature.)
This tool should be used with care, since most of the objects here are usually defined in accordance with company standards & shouldn’t be modified, but it’s nevertheless a useful command to know.