Abraham Lincoln
Because of the religious significance of the name Abraham, it's impossible to say how many Abrahams was given the name in honor of Lincoln. However, unlike names like James, which have been shared by multiple presidents, there was only one president named Abraham, a fact that highlights Lincoln's enormous influence over the country and parents in particular.
According to the Huffington Post, the name Abraham has endured in the same way that Lincoln's legacy has: in 1900, it was the 195th most popular boy's name; more than a century later, in 2013, it was still ranked #183. And, perhaps more than any other president, Lincoln's name is associated with countless memorials, schools, museums, and other civic endeavors across the country.