Somehow my husbands relatives are attached to my name, not his and I can't find how to remedy this.
Where you see the relationship you should also see a small pencil-and-paper icon. That is an edit button. Click it and in the pop-up menu that results detach ("Remove") the person. Generally it is more efficient to remove the child (ie yourself) than remove the parents.
Before you detach yourself, open the profile of one of his parents. Then once your profile is detached from them you can attach him to them.