The Netherlands is a mixture of Dutch, Flemings, and Frisian with Frisian being currently spoken in a small northwest portion of coastal Netherlands.
Miller does not sound like it would be an extraction of any of those but Jakob, of course, does.
It is possible that Mulder (Dutch: Miller) or Mueller (German: Miller) were changed at some time in the past.
The coastal Dutch were directly across the channel from England and were great traders. Sometimes the contact with the English caused them to Anglicize their names for business reasons.
It is also possible if they came to America on an English boat by way of England the name change could have happened there.
Another possibility is that Jakob was of English extraction whose family had immigrated to Holland sometime in the 17th century. That happened pretty frequently because of the religious wars in England at the time.
The interesting thing about this is that I found the Dutch link on the internet on a genealogy link from some town in the Netherlands. The only part of the site that was in English was the part pertaining to my ancestors. Now, I can no longer find the link.
I was trying to trace the history of this blood dyscrasia and found that I had the Miller family in my ancestry, several times. I had already come across a hand written note of my grandmother’s, saying that her paternal grandmother’s family was Dutch from Holland, but I thought that had to be wrong, until this Dutch family tree popped up.
Yes, they could have been English that emigrated to Holland because I believe that they were Calvinists. That might make sense. I guess they could have just moved there, the same way that they moved to Pennsylvania.