You know how it is: you want to be accurate and respectful to a great artist, but you also want to be understood (and not to look an idiot).
Well, good luck with saying van Gogh, then.
When in Rome do as the Romans do, we're told. I don't actually know how the Romans pronounce van Gogh, but a Parisians tend to say van Gog, a Londoner might say van Goff, and an American could well say, for what reasons I cannot imagine, van Go.*
As for someone, like van Gogh, from the Netherlands, if he were speaking to a compatriot then he'd probably say something like fun Khokh, where the kh sound is the throat-clearing noise you hear at the end of loch and the f of fun is really much close to a v sound than a normal English f.
So: how should we say van Gogh?
Luckily we can go to the horse's mouth, so to speak. Vincent van Gogh lived in London and in France, and he found a simple solution. You can even see it on his paintings.
In a letter to his brother Theo, van Gogh wrote 'my name must be put in the catalogue in the way I sign it on the canvases, i.e. Vincent and not Van Gogh for the excellent reason that people here wouldn't be able to pronounce that name.'
(I notice that van Gogh capitalises the Van in his name, and that's another reason to go with Vincent.)
I suppose we could call Vincent's solution the Leonardo option...
...though, now I come to think about it, people don't go around saying Leonardo da vincky, do they?
Name To Say Today: probably not van Gogh! The name Vincent comes from the Latin word vincere, which means to conquor.
*Rather sweetly, here in Britain Van Go is a vehicle hire firm.