I'm traveling to my home country but my passport and green card have 2 different last names. Will taking my marriage certificate be enough for when I re-enter the US?

Immigration officer can get access to all your info just by swiping the card, so they know your names and everything else about you. If it makes you feel more confident, then take a copy of marriage certificate with you.

Make sure your name on the ticket is exactly the same as in your passport... good luck.

Thank You :-)