Apparently, in the fifteenth century, Turkish traders started supplying England with the helmeted guinea fowl, Numida meleagris, a bird found wild in East Africa which had been domesticated there for about 4000 years and was so named because of the strange bony structure it has on its head. It had been introduced by the Romans 1400 years earlier, but had been lost with the collapse of the Roman Empire.
These traders were known as Turkish or Turkey Traders and, by the sort of popular misunderstanding which helps create new words in a language, these birds became popularly known as turkeys. They were a popular meat at Christmas because they tasted good and had a fair amount of meat on them.
Later, when the distantly related wild bird, Meleagris gallopavo, now know as the turkey, was introduced from the New World, because it looked and tasted a bit like the 'turkey' it was mistakenly also called a turkey. As the helmeted guinea fowl fell out of favour, the name transferred to the New World bird.
So, a New World bird came to be known indirectly by the same name as a country with which it had absolutely no direct connection.
Like so much else with the European Yuletide, midwinter festival onto which the Christian Nativity myth has been grafted because the church couldn't bear being left out, turkeys have nothing to do with the Bible stories on which the myths are based. Nor do holly, ivy, mistletoe, plum puddings, mince pies, dates, figs, the giving of gifts or even the season of goodwill to all men, wassailing and yule logs.
Have a Cool Yule.