Hi Rana: a couple of possible suggestions for you here.
1) "Is there a setting or rule that would override the row name to equal the member number/name/description?" None that I am aware of (although I welcome others feedback). Best practice would be to populate descriptive row names as you are building the cube view.
2) Instead of the Designer, if you go to the Advanced tab -> Rows: you'll get a slightly easier to navigate list. That might be a starting point.
3) I have to ask...hundreds of row sections in a cube view? Can you use member expansions instead of making them individual row sections?
4) If going through with the update to the row names is a requirement I'd approach this by exporting the cube view to xml via Application Load/Extract, writing a PowerShell (or Bash) script to do the structural editing for me, and then re-importing via Application Load/Extract. ChatGPT typically nails these types of scripting questions for me.
Edit: if you go this route, make sure to backup the original cube view / import using a slightly different name.
Cheers, db.