@R_T - The support team’s response to me:
Thank you for your patience, I managed to discuss your request with the responsible team!
I received confirmation that for the Public boards shared with Comment rights, indeed there is an old feature that allows setting the Guest Name. However, it's also true that this didn't and doesn't cover Password protected boards. I was informed that this feature wasn't touched and the team kept it available when they were working on Beta of Guest Names associated with Publicly editable boards.
I was told that the team would discuss this feature with our Workshop Team again to check on the future of the old version for Public boards with Comment rights. Sadly, according to my colleague, even following the discussion, this task will not be prioritised for now.
In summary, it looks like the Anonymous-Guest-Naming-on-Comment-only-boards feature never worked with password protected boards (password protecting came later). And once the Allow anonymous board editors to rename themselves for the duration of a session feature is out of beta, they may or may not build in the option for comment-only guests to rename themselves on a password protected board. While this answer may not be ideal, at least we know and you can plan around this scenario.