Curious facts about the "Turkey" bird:
First. You are lucky to have access to wild turkeys. I live in Europe, and the turkey is an American bird. We have turkeys yes, but not of the wild variety.
The first Europeans to meet the bird were the Spaniards, in Mexico, in the early XVIth century. The Aztecs had already tamed them and the Spaniards readily adopted the big tasty bird and introduced them in Europe.
All the European Nations started breeding the bird, but, all of them named it erroneously.
In Portugal we thought the bird was coming from the Spanish colonies of Peru. And so, that's what we call it. Originally, the Peru chicken. Nowadays we just call it peru. The French, they knew it came from somewhere in the New World, then called the West Indies, and so they simply called it l'oiseau d'Inde , meaning the bird from India, simplified nowadays to dindon. The English, were at the time in war with the Spaniards. So, their birds arrived by a sort of backdoor. It was the Mediterranean traders that started their trade route in Turkey that brought the bird into England. It ended up being known as the Turkey bird, turkey for short.
During the rest of the XVIth century the whatever you call it bird became so popular that the first English settlers in Northern America took specimens with them to introduce it to the New World.
It was a great surprise when the call of their captive tamed turkeys was answered by their wild brethren in the woods.