Good question. Originally, the name was Norwegian, so it revolved around patronymic naming for a time. When Dirck Volckertszen came over on the boat around 1630-ish, he was obviously not a Fulkerson. But he was the son of Volckerts, and you would imagine that his children became Dircksen? - Close - they became Dircks. However, there was a Volkert Dircks, whose children became Volkertszen. And from there, the patronymic naming was broken. His children were Volkertszen, next generation were Folkertsen and by the next, it was Fulkerson. So lots of variants around until the 1700's, where Fulkerson became the most common spelling.
And the closest translation of Fulker or Volker - I believe is "smith", which is funny, because Dirck was a carpenter. One of the first carpenters to come to New Amsterdam and who probably built some of the first homes for the workers in New Amsterdam/New York City when it was just getting started.