time machine will not start back up due to two disks named Macintosh-HD-Data

Yeah, that is definitely out of order.

Obviously only one of those "Macintosh HD - Data" volumes is current and proper.

When you select these different volumes, you should find one has the Finder face icon displayed on it in the pane to the immediate right, indicating it is the current startup volume. And one of the "... - Data" volumes should display a house that indicates that is the location of your current user "Home" folders. Can you identify those?

The others are errant APFS volumes and should be deleted by right-clicking and selecting "Delete APFS Volume..."

You may have to unmount them first.

You do already have your data backed up onto other drives, yes?

A better question might be "Why do you have two volumes named Macintosh HD - Data?"

That indicates an improperly installed macOS and potential trouble, well, actual trouble as you can now see.

Can you post a screenshot of the list of drives and volumes that are displayed when you launch Disk Utility and select View > Show All Devices?

You'll find the Unmount button right there in the tool bar just below the Disk Utility window title.

I was really hoping that the volume "Macintosh HD1" would be your startup drive. I'm not sure if what I've suggested will ultimately work, but it's worth a try. Typically the startup drive is not an indented volume below "Macintosh HD". It usually IS "Macintosh HD". So I'd still see about deleting these other APFS volumes, but don't be surprised if it doesn't pull things together. You may end up having to erase and restore the startup drive once again to fix this properly.

EDIT- What year iMac is this? (Apple  icon > About This Mac)