Rare is the man who would object to being mistaken for a Greek god. That is, at least, if the error occurred based upon his physique. The men formerly known as Joseph and Saul objected nevertheless and not simply because the crowd based their decision not on their physiques.
Barnabas already earned a new name due to his endearing habit of encouraging others as did Paul due to his blinding encounter with the risen Lord. They did not welcome any additional titles. Paul objected to being confused with Hermes and not because that would have meant that he was less powerful than Zeus. Rather he, and Barnabas, believed in the one true God and knew who He was.
I remain uncertain as to the reason for Barnabas being deemed "Zeus;" the Bible, however, explains why Paul was thought to be Hermes. Hermes, the son of Zeus, according to Greek mythology, is the messenger of the gods. Paul healed a man and spoke well. Wasting not a moment, the two servants of the real God spoke up.
In his book, Dangerous Calling, Paul David Trip calls his readers, most of whom he assumes are pastors, to beware of the trap of "self-glory."
The encourager and the apostle both had their opportunity for glory. They declined.
The days of being mistaken for gods of Olympus are past, but not so the temptation for glory-seeking.
Of what are you most proud?
What "fills your tank"?
Do you desire the praise of men?
Do you take care of your body to the point of obsession?
Do you flaunt your IQ?
In the Westminster Confession, the first phrase of the response to the question of our purpose for existence is "To glorify God."
Now that's a great answer!
When we remember that God "makes us, and all of this - sky, earth, sea, and everything in them," we know His power and our place.
Tripp, Paul David. Dangerous Calling. Wheaton, IL: Crossway, 2012.