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USA resident but Mexican citizen with permanent Green card

Explorer C

Hi, I'm traveling to Mexico, I'm a resident of USA with a permanent green card but a Mexican citizen. I went to get my Mexican passport and they would not use married last name (on my green card) because I got divorced, but I still use my married last name. So now I have amexican passport with my maiden last name ( I signed it with my married last name) and my green card with my married last name. I purchased my ticket with my maiden last name. Would I have problems coming back?

can I use my divorce papers to prove my last name? Or a notarized letter? To show I'm the name person? Everything I have is under my married name. Except my mexican passaport. Or can I just use my green card to travel?