"There is nothing in the world more common." *
This subject has already been covered somewhat by Paul Dickfoss in his article, "Spotted Handkerchiefs!" and by Emily at Emily's Vintage Visions, but I'm going to add a little bit more info.
In the 18th Century, these handkerchiefs were referenced by the terms "bandannos," "spotted," and "bird's-eye," (and possibly "India") and seem to have been one of the most common types, along with white and checked.
Bandano handkerchiefs were listed among the wares for sale by Allen Jones in his ad in the Virginia Gazette on Oct. 31, 1771.
In her article "The Indian Origins of the Bandanna," published in the December 1999 issue of the magazine Antiques, Susan S. Bean states that although it was already illegal to sell them in England, in 1720 the British East India Company began sending bandannas to England to be reexported to the colonies and Europe. Like other Indian fabrics, bandannas were imitated by European textile manufacturers. Bean also notes, "The popularity of snuff in the eighteenth century increased the need for pocket handkerchiefs, particularly dark-toned chocolate-colored and red bandannas."
"bandannos, which are spotted handkerchiefs" - George Armstrong, Robert Armstrong, William Cotterell, Theft > theft from a specified place, 13th January 1773