In most cases, passports are not showing exactly the same names...
I am dual Swiss and IT, and while in Italy my married name does not exist (a woman always keeps officially her maiden name, and the married name is added as a postscriptum at the end), in CH I have to add the married name after the maiden one.
To add insult to injury

the divorce transcription takes such a long time that I am Ms. Maiden with First Husband at the bottom on the IT, I am Ms. Maiden on the CH one... and my current legal name is Ms. Maiden Second Husband.