You set your character background at character creation, but there's also the first conversation with Callisca. What you say ends up in your biography. Some people in the game will react to this - I'm not going to list those in this thread.
Some backgrounds hide professions you wouldn't expect there. Now you can choose something you like the most without restarting. Maybe I should update the wiki.
Aristocrat (all except The Living Lands)
Artist (Old Valia)
Clergyman (Aedyr)
Colonist (Aedyr, Old Valia, The Living Lands)
Dissident (Aedyr, Ixamitl Plains, Old Valia, Rauatai)
Drifter (All)
Explorer (Deadfire Archipelago, The Living Lands, The White That Wends)
Hunter (All)
Laborer (All)
Mercenary (all but The White That Wends)
Merchant (All)
Mystic (The White That Wends)
Philosopher (Ixamitl Plains)
Raider (Deadfire Archipelago)
Scholar (Ixamitl Plains, Rauatai)
Scientist (The Living Lands)
Slave (Aedyr, Deadfire Archipelago, Old Valia, Rauatai)