The league renames the loser's team for the entire next season, and the loser cannot change it, no vetoes, no appeals. Every matchup, every waiver claim, every standings screenshot carries the name the league chose. One Reddit league's loser spent a full year as 'Throat Goat'.
The long haul: this is not a one-afternoon sentence. With a time commitment of full season, the punishment keeps paying out (for everyone else) long after the season ends. Long sentences need a written end date and a league-appointed enforcer who checks compliance.