Was is Wolfgang Amadeus Mozart, or was it Johannes Chrysostomus Wolfgangus Theophilus Mozart? What would his friends and family call him?
His baptismal name was the second longer version, following Catholic tradition of having a religious name first (like the conventions in Catholic countries of having Jean Phillipe, Jean Thomas, Jean Claude, etc.), so Joannes Chrysostomus would refer to the Catholic Saint St. John Chrysostom, and Mozart was born on his feast day, so that's the religious name.
Theophilus is the Greek form of the Latin Amadeus, so that's why he would be called Amadeus, and where that came from. Though he never referred to himself as that, except as a joke.
Mozart travelled extensively, both as a child on tour with his father and sister, and later in life, and so would adapt his name to be easier for the people of that country to pronounce, so he would have been called many things in his life. This was a common convention at the time, like Handel who was Georg in German, but called George in English.
As for what his family and friends called him, he was colloquially called Wolfgang Amade (also spelled Amadé or Amadè), which is how is referred to in his letters, and how he signed his name on his marriage contract.