AOS filling and change of passport help!!!

[JV5810]

I got in the US with a B1 visitor visa and am currently filling for AOS and I have used my married name for the forms but my passport is still under my maiden name. Will there be a problem if I change the passport for my married name already while the AOS is in process? If I do change it how will I be able to change the US visa page? because its in a separate sheet and my country's consular office said that they will not change that because that is up to the US.

Please enlighten me whether or not to change it... thankyou