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In the US, each state has different rules about marriages, so it would
depend where the couple married as to whether first cousin marriages were
allowed. I remember, not so many years ago, when 2 grandchildren of a
famous Chassidic rabbi were going to marry. They couldn't legally marry
in NY, so the marriage was held in New Jersey, not far away, in a
football stadium as I remember, for about ten thousand close friends.
The reception was in NY.
Another alternative to the false name is the likelihood that a brother
and a sister's children were married, or two sisters, so that they would
naturally have different surnames. Generally, the marriage record (but
not certificate) would have the parents names on it, so you might not
have all the information possible.
A third possibility is that one of the names was changed (my guess would
be Drozdowitz) to something easier to spell and pronounce. Again, the
marriage record and further research might make this clear.