@Graffito pointed a possible the answer when he mentioned the nobiliary particle:
A nobiliary particle is used in a surname or family name in many Western cultures to signal the nobility of a family.
However, the mentioned de, as well as the common Dutch van are not signs of nobility (contrary to the German Von). However, the wikipedia article continues:
However, in some languages the nobiliary particle is the same as a regular prepositional particle that was used in the creation of many surnames.
So it seems that at least grammatically we can refer to it as a prepositional particle, used in the same way as a nobiliary particle.
Of course, I doubt anyone would know what to fill in on a form if you use prepositional particle as a descriptor of a name field...
As far as usage is concerned, the prepositional particle is considered part of the surname. So
Jan de Vries has the surname
de Vries, not
Vries. In Belgium, the prepositional particle is even used when ordering names alphabetically.