It depends on whether it is indicated in the inheritance notarization at the time of inheritance that the house belongs to the personal property of the registrant after marriage. If so, the house only belongs to the personal property of the registrant and has nothing to do with another person.
If the name is added, it will be regarded as giving part of the property rights to the other party, making it the owner of * * *. So ~ ~ adding a name is more reliable.