In the original When a Stranger Calls (1979), the killer is a child murderer who is a total stranger to Jill (the babysitter, played by Carol Kane).
I don't think we ever find out who the killer is in the 2006 remake, but I doubt that it is her father (unless that's supposed to be a shocking surprise that they're saving for the sequel).
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She refers to him as "Charlie", in her head and with other people. She only calls him "Dad" to his face.
Gepetto
Alexis Ayala played the dad in the movie "From Prada to Nada".
Your dad
Esther killed the dad, but she didn't succeed in killing the boy.