It happens frequently when the purchase is made by the couple that was not yet married. In the Registry only appears as owner who intervened as buyer in the public deed of sale. In order for your partner to be included as a holder in the Registry, it will be necessary to transfer ownership of the property, such as donating half of it or selling an undivided share, being necessary in both cases to grant a public deed and pay the corresponding taxes.
And what happens with the mortgage? It depends.
If the couple does not marry or do so in separation of property after buying and before having paid the entire loan, the property owner will be the sole property owner of the dwelling. If the fees are being paid with funds from both, the non-owner will be paying a debt that does not correspond to him and can claim from the other what he paid. It can be compensated by awarding an undivided part of the house as payment in kind.
If they are married in marriages after the sale but still owing the mortgage loan, the solution is established by the Civil Code stating what will be the general rule and which is the exception.
As a general rule, the property purchased in installments by one of the spouses before the beginning of the conjugal partnership will have the character of privative, although all or part of the price is satisfied with community money. Now, the part paid with property is a credit that must be settled upon the dissolution of the community of acquisitions.
Exception when it comes to the habitual residence, which has been paid with money, part of the property and part of the property in which the property belongs proindiviso to the community of acquisitions and the spouse, with a private character, depending on their contribution to the acquisition.
If the couple was already married when the house is purchased, it will be a property even if only one of them formalizes the purchase before a Notary, if the buyer states so, or if he does not say anything about it, presumably. In both cases, it will be registered in the Registry only in the name of the person who has formalized the purchase, with a marital or presumptively marital property, requiring, therefore, the consent of both, a future sale of the property.
An exceptional assumption is that in which the purchase is made by one of the spouses providing private money for the payment of the entrance (from an inheritance) being in such a case the house in private proportion. However, if your destination is a habitual residence, the exposed rule would apply, otherwise the property acquired by one of the spouses for a constant deferred price will be owned by the partnership or privative according to the nature of the first disbursement, even though the remaining terms have been satisfied.