If you have Dame the Despoiler at a battlefield and the opponent attacks in with a unit that has deflect, can you choose not to pay the deflect cost to avoid having to use her on defend ability?

You don't need to — you can simply target Dame herself instead of the attacking Deflect unit.

Dame's triggered ability says "choose a unit here" — it does not force you to choose the attacker. Since abilities can target their own source (Rule 355.9.c), you can choose Dame herself. Deflect only applies to spells and abilities an opponent controls that choose the Deflect unit (Rule 809.1.c), so targeting your own Dame costs nothing extra. The ability still resolves: her Might becomes her own Might (no change), and she gets +1 Shield.

If instead you wanted to avoid the ability entirely — you can't, because it's a mandatory trigger (no "may"). But you always have Dame as a free, legal target, so the Deflect cost never comes up unless you volunteer to point the ability at the attacker.