There are 3 teams in Gladiabots: the Red Team, the Green Team and the Blue Team.
You can see their stats here: https://stats.gladiabots.com
Teams are automatically assigned to premium players (Steam, itch or iOS players or paid Android players) as soon as they get their first league promotion (meaning when they enter the Gold league for the first time).
Players can't decide which team they are assigned to or change team.
They stay in their team as long as they are in the Gold or higher league. If they are demoted to Silver, they exit the team and will get back to the same team when they get promoted back to Gold league.