This one is a mystery for several reasons - who killed the victim and who is the victim really?
There is nothing in Father Flores' brief POV to suggest that he is anyone other then who he claims to be, but Eve quickly discovers that not all is as it seems with this victim: he as the remnants of a gang tattoo and several knife wounds, which don't make a lot of sense on a priest.
Unlike the previous book, Strangers in Death, Eve doesn't have a suspect until late in this book. A lot of this is due to having to take the time to figure out who the victim really is, since the motive for the murder was about who he really was and not who he was claiming to be.
There is the added confusion of (spoilers!) a copy cat who kills someone else who's a religious figure. This copy cat makes Eve wonder if she got the motive for the first kill wrong - was it less about who he was and more about what he was (or was pretending to be, in this case), a priest?