I believe it should be the same as a dragon's name. For example Miraak has two parts, Mir and Aak. (=loyal guide). The difference is, dragon's name is usually formed from three words (Odahviing = snow hunter wing), but a priest can have two or even one word name like Krosis. I think that's all that's to it!

Krosis is just one word, he's a dragon priest. They're given names that relate somehow to them. 

Thanks Daraya andDovaKiinZaan! This really helps!