There are multiples of the same internal SSD (with "- data" at the end of the name) and it's confusing Time Machine

I just replaced the internal SSD in my MacPro cylinder with a 2TB one. I tried to startup in recovery mode and transfer my latest Time Machine backup to my new SSD, which was this whole big ordeal that I finally gave up on, but anyway, the point is that I had to reformat my new internal SSD, and when I reformatted it, I didn't know which drive to select, because startup drives always appear twice in Disk Utility now. And I don't mean two partitions, I mean it appears once with the drive's normal name, and once with "- Data" at the end of the name, and they both show the full 2 TB of space. So just to be safe, I reformatted both of them before installing Monterey. But unfortunately, my system drive now appears three times in Disk Utility, two of which have that "- Data" at the end. And more to the point, every time Time Machine tries to run, I get this error prompt:

Two of the disks to back up have the same name. Rename one of the disks named “MuddyMudskipper”.

So I have to eject that extra drive named "MuddyMudskipper - Data" to get Time Machine to work, but it just reappears every time I restart my computer. I'm hoping someone can give me a more permanent solution, and also, tell me what I should have done in the first place, so I'll know how to handle that duplicate volume in the future. Thanks!

• Mac Pro (Late 2013)
• 3.5 GHz 6-Core Intel Xeon E5
• 64 GB 1866 MHz DDR3
• macOS 12.7.2