When we arrive our passports will still state our original names and that we are not married.
So you are not married.
I don't know which country you are from, but at least in France between the instant when the mayor states "you are married" and the time this information arrives everywhere it takes an indefinite amount of time.
In the most optimal case, you will get papers (in French) wording out the fact that you are married. There are about 7 toms of exceptions to that.
Before that information gets on the passports, if it gets there at all(1), it takes all the time above + the time to get a passport.
So if you state "we are married", you may not have any paperwork for that.
This is beyond the case that at the moment of the application you are not married (you would need to check whether you need to update this information or not when you are abroad (because you leave on the same day and this will be the moment when your married state becomes technically enforceable))
(1) In France each of the newly married can use the name of the other (it is way more complicated than that, but that's the rough rule). You may want to have on your passport DUPONT ép DURAND which means that the initial name is DUPONT and the name of the other person is DURAND. Again, between the moment when you celebrate at the town hall and the moment you see this an indefinite time passes.
It gets funny when your name is SILVERSTONE and your spouse ELONGICURE and you have on your passport SILVERSTONE ép ELONGICURE and get a ticket as SILVERSTONE ép ELO because it got trimmed. This ensures wonderful memories of explaining French stuff to border control.