We're part of a Mega gym (3 locations). It's unavoidable sometimes. They try to have the teams compete in separate divisions (i.e. Large and small) but sometimes our teams compete against each other. Even in our main location we have 2 M1 and 2 Y2 teams (plus our other 2 locations each have a M1 and Y2 team) so we can have 4 teams from our gym as a whole in each division if it's not broken up by A, AA, AAA divisions. Sometimes they're in the same division. We don't really have a say what division we get placed in. The EP tends to decide.
We've also had it where they announce awards and they don't announce the team name and we're left wondering who won. lol It's just part of being a mega gym. We don't really have any rivalry. We treat any of our teams as a win for the gym as a whole and don't focus on the individual team.
As for why we don't consolidate our teams. 2 of our gyms are 30min apart but during rush hour traffic it's longer. It's easier to travel to the gym closest to you because they're in different cities. Our 3rd gym is 5hrs away. Since our area has the larger comp's they come here 4 times a year for showcase, Nationals and 2 other large comp's.