In the USA, you can get a passport in any name by which you are customarily known, provided that customary usage is well established enough to satisfy other needs for identity,. For example, according to Wikipedia, Teller (of Penn and Teller) has a passport bearing only the name “Teller”. When applying for such a passport, you would need to present documentation that supports the fact that you are widely known by that name.
So, to the OP, it would be very easy to have separate identities in two countries, but that would be no practical import unless you were a fugitive and the touchy subject of extradition reared its head. Your identity in any country is nothing more than whom you are known to be within that country.
If woman has dual citizenship, and gets married, it would be trivially easy for her to change her name on only one of her two passports. Canadian women are no longer expected to change their name upon marriage, so this would not attract any attention.
However, in general, dual citizens are not “entitled” to two passports. Each passport-issuing country probably stipulates in their laws that a person bearing a passport may not possess a pasport from another country, but this is rarely enforced and practically unenforceable.
I know a woman in Moldova who also has a Romanian passport, and which one she uses depends on what countries she plans to travel to, but once you start out with one passport, you pretty much have to keep using the same one for the duration of the trip, otherwise you wind up doing some ‘splainin’ to some notoriously unforgiving immigration officers if you try to leave a country for which you have no entry stamp,
As I said, the Canadian application asks about other passports you have (from other countries) and nowhere suggests you must stop using them or surrender them. There have been whole threads on dual citizenship, renouncing citizenship, etc. General consensus seemed to be USA doesn’t care either.
the only time I wonder if it is relevant to authorities is when the court orders you to “surrender your passport” as a bail condition. technically, IIRC, the passport is the property of the issuing government and so another government probably has no right to order you to surrender it - assuming they would even know. Does the passport office routinely look up or share that information?
Yes they are, says the alien who has a list of 22 aliases in the US’s database (as of last entry into the country and assuming they haven’t started adding things such as board names). When I look boredly into the camera while sticking my finger on the little reader, the database pops up that list of aliases, my dates of entry and exit, what types of visas I’ve had…
Note that as far as I know, the database is “local”: it doesn’t include data from any other of the countries I’ve been to. It includes my Spanish ID# but only because that happens to be my passport number, if we had different numbers for both it wouldn’t.
I have two passports. I generally use passport A to enter country A, passport B to enter country B, and whichever of passports A and B has the less onerous visa requirements to enter third countries. Never had any problem. Neither the A authorities nor the B authorities have any objection to my holding a second passport.