Here's my experience :
My french passport says " 1st name" " maiden name" ép ( = épouse = spouse ) " married name".
Because of that, the embassy in Paris issued the I551 in my maiden name ( even though I was married, and my US driving licence says : " 1st name" " married name" which is my legal name since I got married). I had gone to the local SS office for the change, and then I went to the DMV.
I called the embassy to make sure that was not a mistake. They said they had to do it this way because of my passport.
Then of course, my real GC arrived with my maiden name.
So far, I haven't had any problems. On my first day at work, I showed my GC and a marriage certificate and that was it.
I personnaly do not see for me any reason to change my GC.
If I wanted to, I am not sure I would have to pay the fee : my legal name at the time was already my married name, so is it a "mistake" from USCIS despite my passport? I don't care.