I have this exact situation. My passport is in madien, work permit in madien, passport is amended on last page for the married name. I use married name and it is my legal name for SS#, DL - UK and US, all credit cards, bank statements etc. I book all my plane tickets in my married name. It's never been a problem for me just point them to the back of the passport where the amendment is. I also never carry my marriage license with me - not a bad idea I guess but haven't needed it so far.