Ventura docs for M2 Macs in this comment: https://gist.github.com/henrik242/65d26a7deca30bdb9828e183809690bd?permalink_comment_id=4555340#gistcomment-4555340
Old Monterey docs in this old revision: https://gist.github.com/henrik242/65d26a7deca30bdb9828e183809690bd/32c410e3a1de73539c76fa13ea5486569c4e0c5d
Solution for Sonoma: https://gist.github.com/sghiassy/a3927405cf4ffe81242f4ecb01c382ac
On a working MacOS system, one would download and create an install Image on a USB drive and install using that drive. Apple support documentation has instructions - a google search is best for more details.
The rename to another folder name doesn’t matter, as long as it is different that the original. The system only looks for the original name and does not search for other names folders to try to figure out it has been renamed.