This is what haman was also saying:
The Gemara says Shahi Pahi in context of haman saying that we don’t respect his laws. But remember that the Persian word for King is Shah. So Haman was in essence saying that they make stupid rhymes with your name (Southern Persians who live in the Pars province still do that). Haman was saying that not only do they not respect your laws, they don’t even respect you name, and the make fun of you.