Getting back to the example I used above, there are two sources for her. One does not provide her maiden name at all and yet tree after tree repeats this. They also do not indicate her parentage. She is listed only as Mary arriving with her husband from Ireland, so already married. (a DAR tree). The husband's name is found spelled three different ways but I have no known connection to that surname. Her birthplace appears to be assumed by her point of departure (as an adult).
The other source (AGBI) presents a Mary Bradford (born in Connecticut in 1690). There may be some relationship there.
I suppose it is possible that she married a mariner and was born in Connecticut but also departed from Ireland on a ship with her husband. I am trying...really.
Anyway, the question remains do I follow the surname or her.