[stilist]

You’d do it lowercase in van Goch’s name because it’s the correct way to write it for him. See https://en.wikipedia.org/wiki/Tussenvoegsel

[LegionMammal978]

Of course, for someone so well-known, it's easy just to look it up; I was just using that name as an example. But in general, particles in names like "van", "von", "de", etc. might be properly capitalized one way or the other, and it can be impossible to tell which without a close understanding of the author's nationality (which in turn can very difficult to determine).