What is the best use of the apostrophe in a church name when the church also "possesses" something? [duplicate]
In Ireland, a parish might have the name "St. Michael's parish". However, their GAA club would be called St. Michael's GAA club.
http://en.wikipedia.org/wiki/St._Michael%27s_GAA
So, I would consider St. Mary's Basketball Team to be correct.
Any difficulty can be removed by writing St Marys basketball team or St Marys Church basketball team. Affiliative use seems to be one area where the apostrophe is disappearing, and no bad thing either.