Are you required to activate Dame The Despoiler's ability upon defending?

Yes, it is mandatory. Dame the Despoiler's Empowered ability — "When I attack or defend, choose a unit here. Increase my Might to its Might this turn, then give me +1 [S] this turn" — does not contain the word "may". Per Rule 383.3.a, triggered abilities that say "you may" are optional to place on the chain, but those without it are mandatory. When Dame gains the Defender designation during combat, her trigger must go on the chain, and upon resolution you must choose a unit at that battlefield, set her Might equal to its Might, and give her +1[S]. You cannot decline or skip it.