This is an interesting question and I cannot answer most of it. I believe your example (Alexander and Philip) was meant to be arbitrary, but I will address it for it is quite an interesting conversation piece.
Olympias, Alexander's mother, was not fond of Philip and neither was he of she. She was a member of a cult that worshiped Dionysus and believed that Alexander was conceived by Zeus, not Philip. Philip married a Macedonian woman and bore a son to his new wife, Cleopatra. The son's name was Caranus. With regards to what Alexander called Philip during his life is unknown and cannot be known. For a short period, Alexander commanded a wing of hetairoi under his father. Perhaps in this case he called him general?
Once Alexander ascended to the throne after the assassination of his father, he set out to conquer Persia. The death of his father is still surrounded in mystery with many historians believing that Olympias plotted the murder and may or may not have included Alexander. The reasons are hardly relevant for this question. It should be noted that later in his youth, Alexander and Philip did not get along. The drinking binges daily often resulted in fighting, wrestling, etc. One night, Alexander and Philip were having a rowdy party when Philip flew for Alexander aimed on hurting the young heir. Philip, drunken, fell which Alexander cried out after, "How is this man to lead Macedonia in to Persia hen he cannot traverse from one couch to another?"1 Alexander began to believe that he was divine. After "liberating" Egypt and being made Pharaoh, he set out for the Oracle at Siwa to confirm his involvement in the assassination of his father. Here, the priest addressed the king, and many different accounts exist. The one that is worth mentioning is Plutarch's. Plutarch claimed that the priest attempted to greet the king in Greek and say "O Paidon" but said "O pai Dios" instead (My son vs. Son of Zeus).2 Alexander took the mistake to heart and from then on referred to Philip II as his "so-called father."