I guess because someone just called it that one day. Like the Oscars awards for movies, actors, actresses and all that one of the ladies looked at the award and said it looked like her Uncle Oscar and the name stuck. Also the name America was the first name of the map maker for Columbus. Actually his real name was amerigo vespucci. Now if they used his last name for the land that they found we would now be called the United States of Vespuccia. Consider this in an alternate time line they used his last name to name the this land America the beautiful would now be Vespussia the beautiful and we would be the USV and not the USA.
The reason why New York is nicknamed The Big Apple is because the name apple was used in reference to the many racing courses in and even around New York City. Apple referred to the prizes being awarded for the races as these were very important races and the rewards were substantial. Read more at http://en.wikipedia.org/wiki/Big_Apple.
There is no solid answer to the origin of the nickname there are many different storys behind it none of them have been proven true the most popular and accurate is the reference in a book by Edward Martin written in 1909 it states "Kansas is apt to see in New York a greedy city. . . . It inclines to think that the big apple gets a disproportionate share of the national sap" I hope this helps.
The phrase "big apple" originally denoted "something regarded as the most significant of its time," and was first applied to New York City in reference to its highly regarded horse racing circuit. Has nothing to do with apples from New York...