I can see that being another thing that bugged Elizabeth and not Philip, the fact that they've probably had people shorten their name without thinking about it because their names have such obvious shortened forms. For Philip he probably liked it when guys he spoke to carelessly called him Phil because they couldn't be bothered with the whole name, and so he started using it. For Elizabeth she probably would take it as pushy if somebody casually called her "Liz" or "Beth" or "El" at the playgroup. So now she always introduces herself as Elizabeth and Philip's right there with the "Call me Phil" introduction.