What's in a name?
Perhaps your Hungarian family named their children by tradition, naming their first son Andras (Andrew), their second Janos (John), their third Istvan (Steven), a first daughter Maria, a second daughter Elizabeth, and so on.
PERHAPS INSTEAD THEY USED NAME DAYS. Children could be named based on a calender of saints celebration days, Catholic saints, and the calender would differ from the saints celebration days calender used in Poland.
A bride had her choice of what her name would be after marriage. She could keep her maiden name. (When I do Hungarian genealogy research I find that the maiden name is used in birth and marriage records. I do not find notations that tell me that this person continued to use the maiden name however. I believe in small towns where everyone knew everyone it was common knowledge.)
A bride could also keep her given name and use her husbands last name as we do most of the time in the United States (where some brides choose to keep their maiden name). However, in Hungary the family name is the first name and the given name the last. Therefore someone called Maria Szabo in the United States would be called Szabo Marie in Hungary.
Another option : The bride could be called her husband's name such as Istvan Szabone (the ne suffix at the end) as her official name, though her friends would still call her Maria.