Synonym of Dream Interpreter

The exact word that you are looking for is Oneirocriticism.

Oxford Dictionary defines Oneirocriticism as

: The art or practice of interpreting dreams.

Merriam-Webster also backs it.

NOTE: Oneirology is a scientific study of dreams and it is different from Oneirocriticism.

On the other hand, Oneiromancy is divination through dreams i.e. you see dreams sent by God or demigods and predict the future.

Oxford Dictionary defines Oneiromancy as

:The interpretation of dreams in order to foretell the future.

Merriam-Webster also back it.

From wiki, Oneiromancy (from the Greek όνειροϛ oneiros, dream, and μαντεία manteia, prophecy) is a form of divination based upon dreams; it is a system of dream interpretation that uses dreams to predict the future.