We generally remember and refer to people by name, not by title, and by convention, the title is not permanently attached to every reference of the person's name.

We normally drop the title when discussing rulers: the fact that we reference their regnal name and number already implies their rulership and adding King, Queen, Emperor, etc. is unnecessary. By convention, when we refer to the wives of Henry VIII, we know that he is King Henry VIII. We don't need to say "Emperor Nero" when referring to Nero, or Emperor Napoleon when referring to Napoleon Bonaparte. In historiography, it's simpler to use regnal names and numbers plus the country where appropriate (e.g. Alexander III of Macedon, William I of England), with monikers to distinguish historically recognised figures (Alexander the Great, William the Conqueror).

We do the same with most titles today: an article might introduce "President Trump" as a formality, but use "Trump" for the rest of the piece. Likewise, we know Winston Churchill not as "Prime Minister Winston Churchill".

Thus, Alexander is indeed recognised as a king (specifically, basileus) of Macedon. But if you want to use his full title in every mention of his name, have fun writing out Alexander, Basilieus of Macedon, Hegemon of the Hellenic League, Pharaoh of Egypt, Shahanshah of Persia and Lord of Asia.