Since your name check is clear (make sure you get notice in hand, not some phone call, sometime they may screw up. see 這裏.
Depends on the Court and your PD, if your PD is current, try to settle the case with AUSA, tell him/her that your name check is clear, ask them to push USCIS to solve your case. Different story is your PD is not current.
Not sure why your lawyer want to push hard for details. One motivation is that became prevailing party so you can claim attorney fee back, but it is dangerous if you are in some hostile Court, they may dismiss your case for lack of jurisdiction, then you get nothing-- your case still be still pending