American Resident with a Passport with different Last Name

Hi, I'm a peruvian citizen with an american resident, but my last name in my green card and driver license is diferent of my peruvian passport (single) that is the one that I will use to get the visa. Do you know if there is any issue with that, some please says that is a problem. My plane ticket and invitation letter have the same name as my Peruvian Passport. Thank you.