It is explained in Chassidus (and if it is, like, REALLY, extremely important to you then I’ll gladly dig up the sources, including the sources in Nigleh — i.e. Gemara, Rishonim, other classic works) , based, of course, off of various sources, that an entire inyan is included in its opening, and subsequently in its end. For instance, the beginning of the Gemara will as a rule include within it concepts that pertain to the Maseches as a whole, and its ending can be traced back to it as well, as a sort of “stamp and closure”.
Well, Acharon Shel Pesach isn’t just its own holiday. You see, this is in contrast to, for example, Shemini Atzeres, about which the commentaries (Rashi…) explain, that it is like a King whose son must go away after being with his father for a week. So the King asks him to remain for just one more day; Shemini Atzeres has its own inyan, its own vorts, and so forth. Acharon Shel Pesach signifies the culmination of the entire Chag; that is why in many sources it is related to as a holiday of Geula, of our future redemption. Since the first part of the Chag, Leil Haseder was mostly focused on our redemption from the Land of Egypt, and the continual redemption even today (bekol dor vador chayav adam lehar’ot et atzmo…; hashata avdin…), now this last part is more focused on the future redemption BB”A.
That is why it is called specifically Acharon Shel Pesach, to signifiy that it is the ENDING and SUMMATION of the entire point and Chag of Pesach, that of redemption and freedom from our chains, whether physical or spiritual.
I’ll be happy to provide sources/elaboration upon request.