Your green card has different name that your passport can you travel outside the us?

This is from the CBP.gov website... "Foreign nationals that are lawful permanent residents of the U.S. must present a Permanent Resident Card ("Green Card", INS Form I-551), a Reentry Permit (if gone for more than 1 year), or a Returning Resident Visa (if gone for 2 years or more) to reenter the United States. U.S. LPRs are not required by the U.S. to have a passport for travel, although most foreign destinations will require you to have one to enter their country. (LPRs that are out of the U.S. for more than 180 days are subject to new immigrant inspection procedures as per 8 USC 1101.)" So, should be no problem. The foreign country will check your passport, and the US will check your green card.