Multiple Music Libraries in iPhone Apple Music App

Inexplicably there are two different music libraries in my iPhone Music app. I called apple and they said they had never seen this before. Both seem to be connected to iCloud and reflect updates I make on other devices. None are "manual" libraries that I have added via physical phone to computer connection. I was asked that question by Apple Tech and told you can have multiple libraries if you create manual libraries but he determined these two aren't that type of library.

Has anyone else had this issue or do other people have the ability to toggle between libraries from their Music app?

When I select "library" from the menu bar at the bottom of the Music app I then am taken to a screen (shown below in my attached image) which has Library in big letters at the top left. On the top right of screen across from Library there are three red dots inside of a gray circle. When I click those it shows me two different music libraries and lets me toggle between them. One of them has my former name that I have changed as the title "My Name's Library". I hate seeing it there and also don't want two different libraries. Apple couldn't help. Thought maybe someone else could. They didn't answer how to delete one of the libraries or change the name and said they didn't know why this was happening.

[Edited by Moderator]