1. Van Gogh devoted himself to painting pictures,

2. van Gogh devoted himself to painting pictures,
3. Do you know about van Gogh.
4. Do you know about Van Gogh.
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Do we have to capitalize 'van'?
Which expressions are correct?

Capitalizing the “V” is standard in English, yes.

All are okay as long as you put question marks at the end of 3 and 4.

1. Van Gogh devoted himself to painting pictures,

2. van Gogh devoted himself to painting pictures,
3. Do you know about van Gogh?
4. Do you know about Van Gogh?

In the Netherlands, do they use #2 and #3?

I really don’t know.

In the US, when I see two-part names, both parts are usually capitalized. The only times I see lower case are in some Spanish names. Here are a few examples:

Van Buren
Di Carlo
Le Carre

But ~~> de la Fuente

In English, it is generally recommended to capitalize the first letter of a person's last name, regardless of whether it is a part of their full name or just a standalone surname. However, there are exceptions to this rule for certain surnames, such as "van" or "von." In the case of Vincent van Gogh, who is a Dutch artist, it is customary to lowercase the "van" in his surname.

Therefore, the correct expressions in your examples would be:

1. Van Gogh devoted himself to painting pictures.
3. Do you know about van Gogh.