This seems like it has been discussed before, but not specifically as a feature request. Generally speaking, many users have asked Stack Exchange about "hiding" certain information on their profile(s), or hiding profile links in the UI, etc.
One very relevant discussion about search engines took place a whopping 11 years ago:
My suggestion here is to allow users to choose a "canonical" profile of sorts (but not using that HTML metatag, obviously). What I mean is letting users
noindex profiles from given communities.
The "hide communities" feature is mostly useless, as users have pointed out many times, since the Network Profile still contains a complete list of communities, anyway (and since search engines still see all your profiles, too).
The biggest competitor to SE is Quora, which allows users to emphasize certain "topics" on their profile, and make their profile generally appear in a sort of "topic expert" formatting of sorts. As with many of the complaints about SE, it always goes back to the fact that the subdomain-community approach introduces so many problems...
But in the meanwhile, if a
noindex option could be rolled out, maybe a lot of users would feel more comfortable using their real name in these communities and become more involved.
Even if SE is hungry for page views, I'm not sure how denying users such a feature helps them, because nobody is searching Google for "anon-user-389294"... all the current situation does is reduce trust (and interaction). Thanks!