For a data source, Forebears has a nice system where you can find out various stats about different surnames, which we'll use for this. Using that I calculated the percentage of people with each surname who live in the US [excluding any who aren't known to Forebears.io].

Huckabee 2016!; Click for Larger Version

Huckabee is a very strong winner here, with 3,700 in America, and only 20 in the entire rest of the world, or a 99.5% America surname. No one else is even close to matching him.

You might think that I would have done better to simply pick the name that's most common in America, but calling "Smith" the most American name ever doesn't seem quite right to me.

To give an example of why, most people would say that Ainsworth is a more English name than Smith. This is reflected in the stats: 28% of Ainsworth's live in England, but only 9% of Smiths do.

Interestingly Ainsworth is actually more common in America than England, but only slightly more popular; not the six times more numerous the population differences would suggest, while Smith is pretty close to six times more numerous. The same comparison works for Australia as well; Smith is about how popular you'd expect it to be given our population differences, while Ainsworth is about half as popular in Australia as you'd expect it to be. The conclusion is obvious: Smith is a generic Anglosphere name, while Ainsworth is more of a specifically English name.

For those of you who remain unconvinced, here's total numbers instead, which gives Sanders a slight lead over Cruz, and then Graham, with everyone else much further down:

Sanders 2016!; Click for Larger Version

If you want them, you can download the original data-set and gnuplot script.