While this type of thing SHOULDN'T cause a problem in a perfect world, there is no guarantee that it won't. I have had clients as recently as last week mention that they were given a difficult time upon entering because the name on their passport hadn't been updated to the married name on the permanent residence card.
I would suggest considering whether you want to use your married name, or perhaps a hyphenate of your maiden and married name, on all immigration documents -green card paperwork and passport.
You can try not changing the passport and traveling with this, the green card and your marriage certificate, but there really aren't any guarantees.
Speak with an attorney about how best to handle the green card case.