Doctor Who provides the typical mistaken pronunciation of Van Gogh common in British English.
Wiki provides the native pronunciation of the name in Gogh's native language, Dutch. Which is not English in nature, the two languages being descendants of two different West German linguistic roots.
But since they are speaking English through alien technology...
Tardis Translation circuit:
Real pronunciation aside, notice that the Doctor corrected Amy when she was going to say she's not from Holland (she's Scottish).
VINCENT: That accent of yours. You from Holland like me?
DOCTOR: She means yes. So, start again. Hello, I'm the Doctor.
We hear them pronounce it in the English manner with a SCOTTISH ACCENT because of alien technology translating their translated Dutch-accented French to English for us.
To Clarify the accents:
They are in Arles, France, at the Cafe de l'Alcazar at the Place du Forum (Public Forum/Square). Van Gogh is speaking French, but has a Dutch Accent as he is a native Dutch Speaker. Amy is speaking English, but with a Scottish Accent, since she is from Scotland. There 11th Doctor has a standard "accentless" English accent, Received Pronunciation. The Tardis is translating Amy's accented English to Dutch-accented French for Vincent, and the Doctor's standard English to standard French. On the flip side, Vincent's Dutch-accented French is being translated to Scottish-accented English for Amy AND US. This is why Vincent thinks Amy is from Holland like him, and why Vincent Van Gogh sounds SCOTTISH to the audience.
Same as Donna speaking Latin is ruined to sound Celtic, I mean Welsh, to a native Latin speaker, a Roman street vender, because of the translation matrix not working in those situations.
DONNA: Hold on a minute. That sign over there's in English.
(Painted on the side of a barrow is two amphorae for the price of one.)
DONNA: Are you having me on? Are we in Epcot?
DOCTOR: No, no, no, no. That's the Tardis translation circuits. Just makes it look like English. Speech as well. You're talking Latin right now.
DONNA: I just said seriously in Latin.
DOCTOR: Oh, yeah.
DONNA: What if I said something in actual Latin, like veni, vidi, vici? My dad said that when he came back from football. If I said veni, vidi, vici to that lot, what would it sound like?
DOCTOR: I'm not sure. You have to think of difficult questions, don't you?
DONNA: I'm going to try it.
(Donna goes to a fruit seller.)
STALLHOLDER: Afternoon, sweetheart. What can I get you, my love?
DONNA: Er, veni, vidi, vici.
STALLHOLDER: Huh? Sorry? Me no speak Celtic. No can do, missy.
(She walks away.)
DONNA: How's he mean, Celtic?
DOCTOR: Welsh. You sound Welsh. There we are. Learnt something.