(Devarim 16:1) "And you shall make the Pesach (offering)": Its "making" must be to that end. If he offered it not in its name, it is invalid.

I might think that this also applies to its roasting and rinsing; it is, therefore, written (Ibid. 2) "And you shall slaughter a Pesach": Slaughtering was in the general category (of "making"). Why did it leave (that category for special mention)? To serve as the basis for a comparison, viz.: Just as slaughtering is expressly for the (altar) service, so all such "makings" (must be specifically to the end of "Pesach"), to exclude those (like roasting and rinsing) which are not altar-oriented.

"to the L-rd your G-d": for His name's sake.

"for in the month of Aviv": a propitious month, one which is neither too hot nor too cold. And thus is it written (Psalms 68:7) "G-d settles (the scattered) individuals (of Israel) in a (single) house (i.e., a united congregation). He releases the prisoners (from Egypt) in an equable (month" [neither too hot nor too cold]).

"the L-rd your G-d took you out of Egypt at night": Now did they leave at night? Did they not leave in the daytime, as it is written (Bamidbar 33:3) "On the morrow of the Pesach the children of Israel went out, etc."? We are hereby taught that the redemption began in the evening.