The Romance languages use that name. English uses "Sun", but just as it borrows a ton of stuff from Latin/French/etc., it also borrows "Sol" for its word "solar".

Also, Captain Archer in Enterprise used the name Sol when making contact with aliens.

And in Germanic mythology the personification of the sun is Sól.

In PIE it's sunnōn. In some languages that evolved to some variation of sun or son, in some to became sol (notably Latin). And many use both variations in some capacity

Latins and medieval scientists did. In Italian we call it "Sole".

If you speak Portuguese or Spanish, yes.

I can't think of any English-speaking places that do... but you see it used in "solar", for example.

It's Солнце (Solntse) in Russian.