Aeron Greyjoy is introduced in ACOK (and is later a POV in AFFC), and is also known as "The Damphair".
What is the correct way of pronouncing that name?
Aeron: — ['ɛəɹən] air-ən, like Aaron
Damphair: GRRM & John Lee pronounce it as ['dæmphɛəɹ] damp-hair while Roy Dotrice pronounces it as ['dæmfɛəɹ] dam-fair
Westeros.org said that in the below link GRRM pronounces Damphair damp-hair.
Unlike Tolkien, George RR Martin doesn't provide elaborate pronunciation guides for his characters' names. So there may not be a fully canonical answer.
That said, "aer" seems to represent a sound similar to the English word "air" -- so Aeron more or less sounds like "Air On".
Damphair is a nickname referring to dousing with water as part of the worship of the Drowned God. So it seems fairly obvious this should be pronounced "Damp hair" (ie. we are saying Aeron's hair is damp). In this case, the "ph" should not be rendered as an "f" sound (Aeron Damfair sounds silly and loses the meaning of wet hair).