Was Alexander the Great called Alexander the Great while he was alive or was that a name that historians gave him?

Hi, not discouraging other contributions here, but FYI you can get started on these earlier answers

/u/BruceWareAllen in [When was Alexander deemed "great" and by whom? Also was there a set criteria at the time that determined who could be given the epithet "great"?] (https://www.reddit.com/r/AskHistorians/comments/8f1936/when_was_alexander_deemed_great_and_by_whom_also)
/u/mumpford has more on Plautus in At what point did Alexander the Great start to be referred to as "the Great"?
/u/perdweeb2 has more on Quintus Curtius Rufus in [When did history start calling Alexander "the Great"?] (https://www.reddit.com/r/AskHistorians/comments/834hjj/when_did_history_start_calling_alexander_the_great)