Changing file name

You have to use your operating system to change the file name. It varies from one to the next. In windows, you can slowly click the file twice, the second one will put it into edit mode. Enter the new filename then press enter. Other OS's have different means.

Once the file name is changed, MuseScore will not have it on the recent list, but as long as you don't change the .mscz or .mscx suffix it will be able to find the file using the Open command.

Sometimes it's additional useful/necessary to edit the work title (File->Score properties...) to see the correct file name in a play list (songbook or with an exported mp3 file).

"Save as" should to the trick too.