Hey there! I'm also from Greece and have the same problem since as you know, Greece won't let you change your last name. But to answer your question, yes, you should be good to go. I have taken multiple trips to Greece and other countries with my Greek passport that has my maiden name, ticket booked in that maiden name, and GC in married name. Entering Greece / other countries, border authorities won't typically care what is on your GC. To board back to the US, they'll check your GC but I've never had them ask why the names are different. Once in the US, CBP cares about the GC itself for the most part and I've never had them ask anything about the names. I always carry a copy of our marriage certificate just in case.
Now, what I haven't quite figured out is what to do once my naturalization is approved since I'll have 2 passports with 2 last names but as far as traveling on a GC, you should be okay!