It seems that changing the name only in the Sharing Preference has had no adverse effects.

Time Machine backups have progressed normally and the network recognizes the new name with no issues that I can tell.

On a Mac since 1984.
Currently: 24" M1 iMac, M2 Pro Mac mini with 27" BenQ monitor, M2 Macbook Air, MacOS 14.x; iPhones, iPods (yes, still) and iPads.