Alexander III of Macedon is referred to as Alexander "the great", but who gave him this title? At what point in history was he acknowledged as such and why is he considered so great?
I think the first time he is mentioned as "Alexander the Great" (at least in the sources known to us) is Quintus Curtius Rufus' "Historiae Alexandri Magni Macedonis", this "Magni" has been translated into English as "Great". Here it clearly refers to his talent as a military leader which allowed him to build up a huge empire. Quintus Curtius Rufus was a Roman historian, this book is considered to be written in the 1st century AD.
Btw, Russian historians tended to focus on the word "Macedonis" which is why he is better known as Александр Македонский (Alexander of Macedon) in Russian.
Alexander was called "the Great" by historians shortly after his death in his early 30s.
During his short life, we conquered essentially all of the modern Middle East and Egypt, starting with a base of Macedonia, a kingdom near Greece. In the process, he defeated much larger, mostly Persian armies, in an unbroken series of battlefield victories and successfully campaigns that are studied even to this day. Had he lived longer, he might have united large parts of Europe and Asia under Macedonian rule.
Despite his bellicosity, his rule was mainly benevolent. He treated conquered peoples kindly (relative to his time), and encouraged his Greeks to intermarry on equal terms with these people. Thus, Greek civilization spread throughout much of the Middle East with little further bloodshed. He also supported the development of learning, and his tutor, Aristotle, plus earlier scholars such as Socrates and Plato, were passed along to later generations as members the great minds of antiquity.