An exclusive or constraint is actually two constraints linked together for convenience in the object model and diagram. These are always handled separately in the logic engine. There is a context menu command to split the constraints (Split Exclusive Or Constraint) and another to recombine them.
Constraint names are unique across a model, so these two constraints cannot have the same name. The name shown in the ORM Model Browser is the name of the exclusion constraint (default of ExclusiveOrConstraintX when the exclusion constraint is initialized linked to the mandatory constraint). The Properties Window shows two properties, Name is the name of the exclusion constraint, MandatoryConstraintName is the name of the linked mandatory constraint. I think you're looking at the wrong name.