Death Knights can be different from one to another, you can have one who strives for redemption, one who wats to find their place in the world, one who strives for war and strife and seeks it eagerly or one who just does their duty, and alike. There’s a lot of attitudes one can have as a DK, even if they aren’t anything close to a Civilian or alike. They aren’t death vengeance god thing, or not necessarily at least, but rather most of them being fallen worthy champions, soldiers or fighters who were risen into the torment of Undeath to serve the Lich King, serve the Ebon Blade if risen later, and alike.
Just keep things such as the need to sate their addiction of infliction pain to others, aka Eternal Hunger and alike in mind. Here’s a solid guide some of my friends had made, which is a really good read: