I am from a Finnish family but hold a Swedish citizenship, and have now for some years lived in USA as a permanent resident (Green Card holder). My wife is a US citizen.
For personal reasons (such as me desiring a more english name) both me and my wife recently filed for a legal name change. The little problem with this was that I forgot to check whether my new name would be approved by the Swedish name change laws.
It's not that the surname is particularly crazy or weird, the problem is more that a surname can be denied in Sweden if it is too common (e.g. if someone else in Sweden has it, or if some publicly known person elsewhere has it) AND I have no (relatively-) recent biological relative with that name. The rules for changing the name, when the new name is not from some biological relationship, can be seen here.
Anyway, my question is about that if I want to travel outside of USA.
Can there be problems at immigration when I come back to USA, if my Green Card has my new name and my Swedish passport has my old name?