Depending on your jurisdiction, anyone can change their name to anything, it just requires a petition to the courts. It's only legal marriage that didn't require that of a woman. Although, it may be that common law allows her to do so without the court as well. I'm not sure. But the point it, you don't need a marriage license and officially recognized polygamy in order to change ones name. Though it is possible that doing so in some jurisdictions could get you in trouble of their bigamy laws. Again, talk to local legal rep.
And that's just all for official purposes. There may have been a time you could go by any name you wished in common non-official interactions, though that may have changed in the modern day with new laws regarding identity theft and the like.