In the US, these automobiles would simply be called "vans", or maybe "conversion vans" if they have aftermarket modifications, especially heightened roofs. Is the difference between what you're talking about and something like a Ford Transit (not sold in the US, AFAIK) the fact that the "dayvan" is a passenger vehicle, while a Transit or its ilk is a cargo van? Because I don't think we have any real distinction between that, other than to simply call them "passenger vans" and "cargo vans", and, even then, they're the same model van with seats added or removed. I do see a Sprinter every now and then (badged as a Dodge), but not often, and always as a commercial vehicle. Not that virtually anyone drives vans as passenger cars anymore; that market has largely been taken over by minivans, which I believe you call MPVs (the Renault Espace seems to be the canonical version in Europe), and those are dorkmobiles (no offense, Derrick).
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Bitt Faulk