TL;DR: I don't think there's any point in having a field for a user's real name in their public Q&A profile now that the only two real uses for it, for use by Stack Overflow Jobs and Stack Overflow for Teams, have been removed. Per the principle of only retaining PII that serves a real purpose, this field should be removed.
This came to my attention when I saw this request, regarding the message shown to users warning them that updating their real name on all sites (including Stack Overflow) will change their name on Jobs-related functionality on the site, and that it isn't relevant anymore now that Jobs has been permanently discontinued. This got me thinking: this field isn't really used at all now as far as I can tell.
The only other use of the field on Stack Overflow, previously, was in Stack Overflow for Teams: originally, one's username on Teams sites would be pulled from and synced with the user's set real name on Stack Overflow. However, since 2019, users' profile info on Teams (including usernames) is now dissociated from and no longer synced with their public Q&A profile info. The only real case where it's used today is when a user joins a new Team: the default, pre-filled name will be pulled from the real name on public Q&A profile, but the user has the option to change it separately, and a fallback already exists for when a user doesn't have their real name previously set: they'll be prompted to enter it when joining.
Finally, there's not much use for storing this information on profiles for other network sites. The only case where it is (or was) used outside of Stack Overflow is in the homepage sidebar block on beta sites to invite others by email to use the site: there's an option to either make the email appear to be from one's display name or from their set real name. But an alternative feature can easily be implemented so functionality isn't lost: just make the second option a text field that a user can enter any name they wish. It's also useful if someone wants to use a different name when inviting (e.g. if I wanted to use my Meta.SE-only "Sonic" name if the person I'm inviting knows me better under that). Outside of that, there's absolutely no use whatsoever for one's real name on non-beta sites other than Stack Overflow.
A similar thing was previously done with the birth date field in the profile: previously, this had a purpose, to show the user's age to other users, but that feature was removed in a 2015 redesign. When GDPR was adopted three years later, the field was removed and all information entered into it was deleted, per the new working principle that the only PII that should be stored is that which is actually used: as birth dates weren't used anywhere anymore, the field was removed. The same thing is true today for the real name field on public Q&A.
To summarize, the sole case where it's used on Stack Overflow is just as a convenience for prefilling when a user joins a Team, but a fallback exists for that making it not strictly necessary, whereas in the previous cases - for Jobs and the previous configuration of Teams - it was necessary. (If the feature is still to exist for users joining subsequent Teams instances, it can be pulled from a user's profile on an existing Team they're a part of.) It's not used anywhere on other non-beta network sites, and a fallback can easily be implemented for its sole use on beta sites.
Given the above, can the field on public Q&A be removed? (I should probably add that the same field also exists on Area 51, where it also isn't used anywhere - in fact, in the sole case where one's real name is used there, when committing to proposals, it actually prompts to enter one's real name rather than getting it from their profile. One might argue that Area 51 uses a dated engine, but the birth date field was removed from there as well in 2018.)