I think you should be considered a green card holder right now.
Based on the law, after you married this person (a green card holder or citizen) for certain period, you are entitled to have a green card. Even though the name on the card is wrong by mistake, you, as a legal person, satisfied all the requirements, thus still entitle the right under the law.
Based on the law, after you married this person (a green card holder or citizen) for certain period, you are entitled to have a green card. Even though the name on the card is wrong by mistake, you, as a legal person, satisfied all the requirements, thus still entitle the right under the law.