Experts pls advise - Petition approved with Maiden Name

[h1bquery]

My current passport with married name was issued in 2004 after my marriage. My old passport with the maiden name was cancelled during the issue of this current passport in 2004.

During the current H1B processing, due to a confusion at the employer end, my H1B has been approved with my maiden name. Now I have an approved petition but am in a dilemma over attending a visa interview due to this error. Since, passport is with married name and petition is with maiden name.

I have both my passports with me along with my marriage certificate. Can someone please tell me how to rectify the mistake?