For those interested on the question of age verification and GNU/Linux: be aware that Systemd v261-rc1 was recently released. It now implements an optional birth date field in the JSON user database (see second item under “Other changes”).
The implementation of this field was prompted by age-verification or -attestation laws.
But the field can contain anything at all, so if anonymity is the goal, you can still have that.
This dialog isn’t asking for a legal name, it’s just suggesting using your real name because that’s a pretty normal thing.