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 to pronounce that name?
Westeros.org said that in the below link GRRM pronounces Dhamphair 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).