By providing the false information in the first place, you have negated any chance of successfully challenging the validity of any document - in fact, it strengthens the other party's case against you. You have also damaged your own credibility and any court will be suspicious of your motives.
You should try and settle this matter privately and quickly. By not using your "legal name" in the first place and then trying to use this against the other party, a court will view your actions as being fraudulent in nature. So if this ends up in a court, you will almost certainly lose and will probably have to pay the other party's costs as well.