I would assume the person who destroyed it, but I thought I had read something somewhere that you could give them out among your team
Hi Kevin, the rulebook says the following:
Coin Reward: When an Objective is destroyed, the player who destroyed it will receive this number of gold.
That player may distribute this gold in any way they wish among their Heroes.
So if you destroy an objective you may freely distribute the gold reward among your heroes. Hope that helps.