Surnames in a fantasy world?

So I started out not using surnames in my story (why I thought that was an okay idea, I don't know), but now I do want to use them. How should I go about picking surnames? I thought about going with the 2-word surname in English, as many fantasy surnames are (Warsong, Bluewater, Moonglow, etc), but idk… is it too cliche? They're definitely fun to use, and I can use them as occupational surnames and such, and I also found a fun way to change them when people get married (if they want to, they can interchange parts and have the same last name, but still keep part of their own, so for example, if a Warsong and a Moonglow got married, they might make their last name Moonsong). But still, I'm having my doubts. (Note: I'm not looking to get published or anything, I just want to give them good names, I guess.)

Okay, so I'll probably stick with it, partially to make things easier on myself. Using it to describe traits seems like a valid enough method.

Yeah, I already do that for most of my stuff, like place names… I kind of wanted to try something different, maybe, but idk. I could always vary surname types by region, too.