backend: spelling -> register_name

[superlopuh]

As noted by Chris in #4020 (comment), spelling is not the ideal name for the concept. name is already taken, so I propose register_name. We already have a helper that returns a str called register_name, which I propose to just remove.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 90.19%. Comparing base (b58cfb8) to head (add4fbd).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4021      +/-   ##
==========================================
- Coverage   90.19%   90.19%   -0.01%     
==========================================
  Files         458      458              
  Lines       58341    58337       -4     
  Branches     5692     5692              
==========================================
- Hits        52620    52616       -4     
  Misses       4331     4331              
  Partials     1390     1390              

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