If a cathedral has to move in a diocese, is it normal to rename the parish?

Pending Vatican approval, my diocese is moving the Cathedral to a neighboring parish. The Cathedral Parish was St. Raphael, the new Parish is St. Bernards. Now, nothing against St. Bernard, but he's not exactly an archangel. So what I'm wondering is, is it the norm to rename the parish a Cathedral moves to (in this case, rename St. Bernard's parish St. Raphael's parish) or is it normal to leave St. Bernard alone and re-dedicate the diocese? Also, since this is the only church in the parish, would it also be normal to rename the church building itself?