Using the term 'troupe' with reference to Morris dancers can seriously injure your health; indeed, it might put your continued existence in jeopardy. Not sure about 'troops' though. Haven't heard that one before. 'Troupe' should only be used with reference to Fluffy Morris.
The rest of us are called 'sides' or 'teams'. Don't ask why - it;s just the way the world works.
JK