Call each team a kingdom/domain or something like that? Name suggestions:
Caelum/Aecor/Solum - Latin derived without going full terra/aqua/whatever air is (literally words for the sky, ocean and ground)
Autem/Deorsus/Medulla - Latin again, but this time it's up/down/middle
Aeras/Thalassa/Edafos - Greek this time. Sky, sea and ground again.
Aela/Adnah/Markaz - Arabic derived. Up, below and middle.
We could also be original and just call them Sky, Sea and Earth in English.