Comment by eclipticplane

When I did a large organization rename (GitHub helped us reclaim a name from a long-since disused account), we were extremely cautious because of this exact problem. Our GitHub organization was named XYZ, being renamed to ABC. We had GitHub rename a separate user, DEF, to ABC. We then picked a low risk time and had browser windows open when we initiated the swap of our new shiny ABC to ABC-old to immediately grab the name and then immediately grab the old name on a new account.