The bird was named after the country.

When Europeans first encountered turkeys on the American continent, they incorrectly identified the birds as a type of guineafowl (Numididae), also known as turkey fowl (or turkey hen and turkey cock), due to that bird's importation to Central Europe through Turkey. That name, shortened to just the name of the country, stuck as the name of the American bird. http://en.wikipedia.org/wiki/Turkey_%28bird%29#History_and_naming

the why for the bird's name really has something with Turks. The bird turkey was originated in america and domesticated by Indians there. In 16th century, when the birds were firstly transported into europe by Turks who then monopolized the trande around the east mediterranean (this is the why for englishmen and frenchmen fighting them later) at that time, the europeans hence called the birds as turkey