I am aware that speakers of British English generally use the term "surname" and AmE speakers use "last name." What I want to know is how long it has been this way, i.e. if AmE speakers ever used the word "surname" and if so, when did they switch to using "last name"?
The usage of "last name" has been increasing in the last 200 years:
In AmE as defined by Merrian-Webster, a surname is referred to as (1) the family name (e.g. Barack Obama) or (2)the assumed name (e.g. Leonardo DaVinci).
A last name, which according to M-W, is not synonymous nor equivalent to surname. A last name is the literal last name in a person's full name.
Therefore, Mr. George Jerry Jones of Ellen's surname could be Jerry-Jones or George of Ellen, while his last name is Jones.
In America, last name only usage became popular in the mid 1800s; one possible theory is the tendency for Americans to be averse to any British tendenacies following the Wars of Independence and of 1812. Another theory is Americans do not have any regency titles, location-based titles (of Ellen, de Gama, et cetera) or multiple family names (as in some romance cultures). American last names almost always are the surname. The need to distinguish last name and surname became less common, as early 1800 Americans prefered the "common man" approach to self titling e.g. John Smith, not John Smith of Boston.
If I find references and sources I will post them; this is simply from memory concerning a discussion once held in my English Literature class in 2007.