The English name for Turkey is derived from the Medieval Latin Turchia (c.1369).
The word Türk in old Turkish means strong. Thus the land of the strong people: Turchia. This word is directly taken from Italian and morphed into Türkiye in Turkish.
When Europeans first encountered turkeys in the Americas they incorrectly identified the birds as a type of guineafowl (Numida meleagris), also known as a turkey-cock from its importation to Central Europe through Turkey, and the name of that country stuck as the name of the bird. The confusion is also reflected in the scientific name: meleagris is Greek for guinea-fowl.
The names for M. gallopavo in other languages also frequently reflect its exotic origins, seen from an Old World viewpoint, and add to the confusion about where turkeys actually came from. The many references to India seen in common names go back to a combination of two factors: first, the genuine belief that the newly-discovered Americas were in fact a part of Asia, and second, the tendency during that time to attribute exotic animals and foods to a place that symbolized far-off, exotic lands. The latter is reflected in terms like “Muscovy Duck” (which is from South America, not Muscovy). This was a major reason why the name “turkey-cock” stuck to Meleagris rather than to the guinea fowl (Numida meleagris). The Ottoman Empire represented the exotic East.
By the way Turks also mistakenly viewed this bird an animal of exotic east and named it Hindi, a reference to India.