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?
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.