In The Conjuring 2, in the dinning room and library where the demon's name appears, is that Mr. Wan's idea or something the Warren's noticed after the fact?
The name "Valak" is given to the demon in The Conjuring 2, and it's the same demon hinted at in the first Conjuring film, as well as the main villain in The Nun. The idea was based on occult accounts of "Valac", a demon mentioned in the Lesser Key of Solomon and a few other grimoires. Depending on the source, it is also spelled Ualac or Valak. He is described as being one of the leaders ("presidents") among demons and of having the power to summon, find, and control snakes.