Entering the US with the intent to marry and adjust status is not allowed. She can use her B1 visa for short visits at discretion of cbp.
Also the USCIS will want to see your tax situation resolved.
Has the beneficiary filed for Adjustment of Status? That's the only way she could be here legally. It can only be filed with the petitioner. She can't adjust any other way. The petitioner definitely needs to notify uscis
The NVC would be able to give you the embassy case number which is different from the USCIS receipt number. You probably have to wait a few weeks to get the NVC case number. Ours took a month to be ready as our timelines indicate.
I would wait a few weeks then use the public inquiry form from nvc. It will tell you whether they have the petition and when it shows ready pay fees and schedule at embassy
On the AOS form use the new name and underneath use maiden name. Request for a new SSN on both the 485 and 765 forms. My wife's new social security card was mailed automatically once the 765 was approved