"Last Name" and "surname"

Between last name and surname, which one is British and which one is American? If I talk with somebody from Great Britain, which one is preferable?

COCA has 507 "surname" vs 1790 "last name". BNC has 315 "surname" vs 43 "last name". So while neither word belongs exclusively to one side of the Atlantic, "last name" is preferred in AmE and "surname" in BrE.

As someone who has lived on both sides of the Atlantic, speaking both American and British/Commonwealth English, I would say that, regardless of what the dictionaries might tell you, last name is distinctly American usage, while surname is arguably British/Commonwealth usage

If you have access, take a look at forms generated on both sides of the pond. In America, I doubt you would find any asking for your surname. In the UK, RSA, etc, I doubt you would find any indicating last name. And trust me, if you said surname anywhere in the US, you may still be understood. You'd probably be excused if you had a noticeable British accent. Otherwise, you'd just sound weird.

The only term that might be equally common in both American and British usage is family name, especially in formal documents and the like. For regular conversation however, I think the above discussion holds.

Surname would be the normal UK term, although last name would be sometimes used and understood.

There is no distinction in American English. Both last name and surname are used, but last name is more common. The dictionaries I checked do not give the term as a British variant.