I am able to get/set the 'BusinessName' of a relationship in a macro using rel.BusinessName,
However, there does not seem to be any property on Relationship that looks like it would hold Constraint Name, even though this a property within the UI
Dim rel As Relationship
For Each rel In mdl.Relationships
rel.BusinessName = "xyz" <--- this is fine
rel.ConstraintName = "blah" <--- this is not a valid property, and no other properties look relevant
For a Relationship object, use the .name property, i.e. rel.Name = "blah"