It's a great bird.. in fact Benjamin Franklin proposed that it be the American bird. The bald eagle was chosen for whatever reason over that
Funny… turkeys (the bird) are called “dinde” in French, which means “from India” and is short for “poule d’Inde”: chicken from India.
Guinea pigs are called “cochon d’Inde” which means “pig from India”. In fact they are neither from India nor Guinea.
India's main official name is India. Bharat (from Sanskrit) is coequal according to the constitution, and Hindustan (from Persian) is also sometimes used.
That's mostly because English is one of the two official languages of India, and even the local native languages (at least as spoken by the English-educated middle class) are heavily influenced by English. Similar to how the Philippines are just called the Philippines (or Pilipinas, the closest approximation that is pronounceable in Tagalog), rather than a native-language name.
Turkiye is okay but Türkiye is not (in English).
Fun fact: India is Hindistan in Turkish which literally means Land of Turkeys. Maybe we should really change. Bharat means spice which is a better name.