Just a number. Remember ICQ? They simple had a number increasing for each new registered account. I mean, if the users still get to set an arbitrary display name, then just give everyone a number as user„name“. Sorted by registration date, this would be the most fair process.
And then yes, there is no validation that someone named „@verge“ is really from TheVerge – simply because there is no such name, and users just need to tell people that 3728348 is their handle. Like a phone number. Unique, easy, fair.