The name Barjona in the Bible
The name Barjona occurs one time in the Bible, and it appears to be Peter's surname (Matthew 16:17). But it may also be a nickname because Jesus uses it to address Simon, to whom Jesus gave the nickname Peter (meaning pebble, not rock).
Etymology of the name Barjona
The second part of the name Barjona probably comes from the Hebrew name יונה (Jonah)—meaning that Peter's father may have been called Jonah. The name Jonah comes from the root group יון (ywn):
And since the Holy Spirit descended on Jesus in the form of a Dove (Matthew 3:16), Jesus calling someone Son Of The Dove, seems quite complimentary.
But perhaps Jesus gives Peter the name Barjona as a pun, as the name Jonah bears a striking resemblance to the verb ינה (yana), meaning to oppress, vex or do wrong:
After all, just half a dozen verses after Jesus calls Peter Barjona, He calls him satan (Matthew 16:23).
Barjona may simply mean Son Of Jonah, but perhaps it means Son Of The Dove, and perhaps it means Son Of The Vexer literally and simply Vexer by implication.