In Spain, people commonly refer to the USA as "Estados Unidos," which translates to "United States" in English. The term "Amrica" is often used to refer to the continent as a whole rather than specifically to the United States.
The reason for two E's and two U's is because Spanish, like Latin, uses two of the initial letters when the word is plural. For example, pp for pages, plural. If it were only one United State it would be EU. Since it's plural, EEUU.