

That’s going to be a problem whatever solution you come up with, because of the federated nature of the lemmy system.
There’s no central authority to hand out usernames, so if two people sign up to different instances with the same username, any design which didn’t attach instance name to each username would fail. The only way around it would be for each instance to contact every other instance which exists, including the ones which haven’t federated yet, and negotiate ownership of the new username, and that’s just not possible
How did you calculate that? The question didn’t even mention a specific speed, just “near the speed of light”.
The kinetic energy for a grain of sand near the speed of light is somewhere between “quite a lot” and “literally infinity” (which is, in a sense, the reason you can’t actually reach light speed without a way to supply infinite energy).