"שחטו שלא לשמו בשבת...“
In order not to be construed as chillul Shabbos, the Korban Pesach must be slaughtered "for its own name," for its own sake and not as any other kind of sacrifice. It must be, in the words of Rav Tzadok HaKohen, zt"l, "on", or linked by name to its origins. Pesach alludes to our chosen status as a people, ex- pressed in Hashem's "jumping" over our homes in Goshen, a manifesta- tion of His "having mercy on us," as rendered by the Targum. We relive
the redemption through the Korban are a Pesach, how Hashem distinguished the us from every other nation and made mor us into on. This clarifies why secre for_morr מיוחס the korban itself_must be the sake of the Pesach to be valid for usua the entire Jewish people!