I have reworked songs many times, then exported them, converting them to new mp3s. Occasionally when I do, the resulting mp3 is an older version of the song. I have to discard every previous version, every mp3, except the new one. Even then, sometimes it will re-name the mp3 the old name. For example, The old name was Overture, John & Charles. The new name is Overture, Bro. Charles. Every time I export Overture, Bro. Charles, the resulting mp3 is named Overture, John & Charles. I have to leave the playlist in Mac Music and go to the main song list, and change the name. Does anyone else have this problem?
First: which version of Audacity you use could be important. Also, which version of macOS. It is always a good idea to mention as many details as possible.
Do you use tags with the name of the song? Then, try to rename this. To be sure nothing is overwritten, move the older versions somewhere else.
Normally, macOS should warn you when a program wants to overwrite an existing file. Some programs do not warn you but add some “extras” to the file name, like “song.mp3” → “song{2}.mp3”
Are you talking about the names of the songs as they appear in Mac Music? Or are you talking about the file names?
If it is the name of the songs in Mac Music, you need to edit the metadata before you export.