Last name missing from passport

Hello Gurus,

I am hoping to get my LC application certified within next few weeks. I have my last name missing from the passport. All my other documents contain my first, middle and last name. My lawyer has told me that the name on the passport should exactly be same as it is on the birth certificate and have asked me get my name corrected on the passport.

I was wondering if anyone have an experience with naming issues at I-140/I-485 stage? I would appreciate your inputs..