Under US law, there's no requirement to ever change names due to marriage. It's a common custom, less common today than decades ago, but it's not required.
As we were checking into this, we found
this page from the US consulate in Caracas regarding travelling on a Venezuelan passport. It says, among other things
If you are recently married or divorced and your name has changed you must get a new passport with your correct name.I don't know if that's only a rule of the Caracas consulate (I suspect so), or if it has wider implications for other countries. Note that it still doesn't mean you have to change your name or get a new passport, just that if you have changed your name, you need to reflect that change in a new passport.
I do know that, if you're not careful, the exact name as written on the passport will become the exact name written on the Green Card, which will become the exact name written on the Social Security card, which will become the exact name written on the driver's license. If you can start the process out with a passport bearing the name she'd like to use, it will make it easier to have that name appear on the later documents.