You can technically apply to make it anything you want, and the set of allowed names should technically be far larger than the set of disallowed ones. But I'm waiting to see if they'll let me take +akkartik rather than +KartikAgaram, so we'll see.
They made it possible to request a different URL for maybe 12 hours after launching custom URLs, but quickly stopped offering it. Probably got inundated with requests. By the time I got my invite (about a day after they started sending them), there was no such link.
Also, they weren't just allowing people to register any old nickname or brand name. It was probably more about letting people make minor corrections.
