When do you have to decide to pay for Draven Vanquisher's triggered ability?

You decide whether to pay for Draven, Vanquisher's triggered ability on resolution, not when the ability is placed on the chain.

According to the official FAQ for Draven, Vanquisher:

• Sequence: When Draven attacks or defends, his triggered ability is automatically added to the chain. You do not pay the cost at this time.
• Resolution: When the ability resolves, you are then given the opportunity to decide whether to pay the 1 Fury Power. If you choose to pay it, Draven gains +2 Might for the turn.

Because the cost is paid on resolution, you can wait to see if the opponent uses any defensive abilities (such as moving a unit away) before deciding whether to spend the power. The "may" in the ability text is part of the effect's instructions, making it a "cost within instructions" that is decided when the ability resolves.