Where are you seeing this?
An image/screen-shot would help.

I'm realizing the reason both names are there is that I made each single stave a group, and named that, hoping it would replace the staff name. But the upshot is, I can't figure out how to change the name of the staff itself.

No need to make a group for each staff. Get rid of the groups and assign instrument names (full and abbreviated) in the score manager for the selected staff.

If you don't want to see any names at all, then go to Staff > Edit Staff Attributes and de-select Staff name (in score and/or parts)

You can also right-click on the staff name in the score and de-select Show. It will still be there greyed-out, but won't print.

Yes, I've done that already. The names are all entered properly in the score manager, and everything looks entirely normal. Yet this is what I have. (I have gotten rid of the groups, so now they are just named, [Staff11] and so on.) It's not the kind of thing that keeps me from getting the work done, but it annoying over time.

What does your score manager look like (image)?

Given the appearance of your Score manager, I do not understand how you would be getting the "Staff #" labels on your staves. Beats me.

....An image/screen-shot would help....

... and a Finale file would help a lot more, but on this (poorly organized) forum you can't attach anything ...

If you really want to resolve this, go to the other, a lot more useful, Finale Forum, attach a short file exhibiting this problem, and somebody will most likely figure it out for you   https://www.finaleforum.com/viewforum.php?f=5