There is no "Green-Eyes Red Dragon", but there are a lot of "Odd-Eyes" cards (one green and one red eye), most of which are dragons, and many of those dragons are predominantly red.
Yugioh card names go a lot wilder than that, though, over an absurd thematic range. From
Interplanetarypurplythorny Beast to
Melfy Catty to
Super-Nimble Mega Hamster.