The USA is a relatively young country, and its first regular issue of gold coins started in 1795. Although most of them have an eagle as a major part of their design, for some reason the $10 piece acquired the name eagle, and the other sizes as double eagles, half eagles, and quarter eagles. The ten dollar gold pieces are therefore known as eagles or gold eagles.
Be careful not to confuse them with the modern $50 one ounce gold bullion eagles. Both are called eagles.
Also see our page for gold commemorative $10 coins.