Club Admins and the Owner can create and rename teams at any time from Club Settings. There's no limit on renaming, but the number of teams you can have is tied to your plan: 4 teams on Club and 12 on Club Plus (see Club vs Club Plus).
If you try to add a team beyond your plan's limit, creation is blocked outright and you'll be pointed to contact support rather than an instant upgrade button. Upgrading itself happens through your billing settings, not from the team-creation screen. Downgrading to a smaller plan never removes or archives any existing teams, even if it puts you over the new limit. You just won't be able to add further teams until you're back under it.