On any platform with usernames, the short ones go first and never come back. There are exactly 36 one-character names (26 letters and 10 digits), 1,404 two-character names and 54,756 three-character names that follow Linky’s rules. That is the entire supply, forever.
On Linky a short name comes with a permanent badge: Legendary for one character, Epic for two, Rare for three. The badge is computed from the name itself, so it cannot be bought, granted or faked.
Then there is the UID. Every account gets the next number. The first ten are Founders, the first hundred are OG. The counter on the home page is the real one, and it only goes up.
None of this changes what your page can do; every feature is free for every account. It changes what your page says: that you were here early, and that you picked well.
If a short name you want is free right now, the odds of that being true next month are not great.