“Van” is part of the surname. It means “of” or “from” in Dutch. It’s similar to “De” prefixed to Spanish surnames.

Yes, but the patent application lists his name as "Halen Edward L Van".

So apparently this was misfiled (under the last name "Halen") or filed correctly, just displayed weirdly on patents.google.com (since it appears correctly on the linked uspto.gov [0]).

[0] http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=H....

So is the rendering on the patent application correct or incorrect?

His middle name was ‘Lodewijk’, ‘Van’ is just part of a compound last name like Von Richthofen or Fitz Patrick, O’Leary, Di Chirico, etc.

I'd heard before they were Dutch born, but still, to hear that Eddie Van Halen was actually called Edward Lodewijk van Halen makes him sound way more Dutch.

And here I was thinking that Jan Akkerman was the best Dutch guitar player ever.

So in that case, why does it make sense to split up a compound name?

Blame it on tradition. Just like today we don’t write “today” as “to day” as used to be the case.