Playing the notes of a basic chord out of order does not change the name of the chord. For example: g, c, e is still C Chord.
The word used for mixing up the order of the notes in a chord is inversions. Inversions are one of your most valuable tools as a church pianist!
In addition to the root position (RH thumb being on the note sharing the name of the chord), every chord has at least two possible inversions.