The family whose surname has evolved to the current form of Polk started out as Pullock or Pollock.(7.8) There is a Pullock / Polk family tradition which states that the family originated within the Muirhead family, much like the Starke family.
The tradition states that a man by the name of Muirhead served as one of the attendants of the King (although there is no mention in the tradition of the manís given name, nor of the Kingís name). In any case, the King and his attendants were marching through the countryside, when an oak shrub appeared directly in the path of His Majesty. Muirhead broke out of the formation and grabbed the plant, pulling it, roots and all, from the ground. For his gallantry, the King knighted him on the spot, and proclaimed that his name would henceforth be: Pullock.
According to the tradition, this man possessing the new surname of Pullock eventually moved his family from Scotland to Ireland as part of the Ulster Settlement. There, a son, Robert Pullock, married Magdalene Trascher. The couple gave birth to six sons and two daughters. Robert and his eldest son, John Pullock, purchased lands in the colony of Maryland from Lord Baltimore. John established a homestead at Locust Hammock in Somerset County. The family flourished in the New World, and the surname eventually evolved to Polk.
Although, like the Starke family tradition, this sounds plausible, the fact of the matter is that Peter, a son of Fulbert, came into possession of a grant of land of Upper Pollock in Renfrewshire from the High Steward. This was during the 12th Century. He took his surname from the name of those lands (in the same way that Willielmo de Muirhead had), and therefore Peter Pollock, son of Fulbert, was the progenitor of the name.
7.8 Information on this legend comes primarily from the website of the Thornton family at the URL: http://home.forbin.com/gwinslow/thornton/wga12.html, maintained by George H. Winslow, Jr. Additional information was derived from the book, The Surnames Of Scotland: Their Origin, Meaning, and History, by George F. Black 1946, p 666.