Acceptance: You accepted your fate and chose the name Douchebag yourself
When you first go into the magical realm which is Cartman's backyard, Cartman will ask you for your name (type in whatever you want), he will then ask if you chose the name Douchebag. Select "Yes", then he'll ask if you're sure you want to be called Douchebag. Select "Yes," again. Cheevo will then pop.
Note that even if you select "No" for both options, he'll still call you Douchebag. Might as well pop an achievement by selecting "Yes" both times, right?