Well, not really. Age verification doesn't have to, and IMO should not, lead to a linked identity. Just a blind check "are you a real human older than X years old? Yes! OK". That way you get the benefits of age restrictions and real human validation, without any of the potential privacy ramifications.
But to be clear, most real people's online presence is under their own names (or linked trivially to their own names, like a cutesy turn on their name for an instagram handle that is linked to their Facebook account which has their full name). It's already possible, and done, to track your public social media presence and interactions. Places like HN and even Reddit are much more niche than that.