My understanding of this is that Elmir is essentially what was left of the Profound Darkness escaping to Omega and trying to conjure up something as "close" as possible to its previous host (Persona). However, I will be leaving it at that for now because I feel that Episode 6 (there is a very "simple" question I can ask that will be a spoiler) has some very big spoilers that have larger implications on this so I will be leave that there for the time being.
So in that sense Elmir is the embodiment of the Profound Darkness which is why he has Dark Falz-like powers and a Dark Falz-like nature without a proper host like all the others. With him having the powers of all five Dark Falzes you will be seeing more of him as he is etched away as a "memory" of Omega (those hints being realized in the next weekly update for a new Dark Falz battle).
I believe he was saying he was Persona just to provoke the player so as to attempt throwing off suspicions because the player and Persona have a clear connection and Elmir shows very little of that connection if at all (and if you are aware of the climax to Chapter 6 in Episode 5 you are aware that Elmir is incorrect).