As for the Indian god, it translates to just Гаруда. Bald eagle - белоголовый орлан. But белоголовый means white-headed, even though bald is лысый. Also, eagle can be both орлан and орел. We have a really complicated language 
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In my native language, ಕನ್ನಡ, it's ಗರುಡ 
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