Day two of the All Saints Octave is known, among the Papists, as All Souls’ Day. A lot of Anglicans use this term also, though what our prayer book actually offers for November 2nd (on page 709) is the optional Commemoration of the Faithful Departed. Granted, that rolls off the tongue far less easily than “All Souls”, but it’s more theologically accurate: we can only commemorate the faithful departed, not the damned departed.
Another reason to consider avoiding the name “All Souls Day” is because of the false doctrines that the Papists put forth with respect to this day. They teach of a place of Purgatory, where most Christians souls go after death, to complete their process of sanctification and finally be completely purged of their sins. Although traces of this sort of concept are almost see-able in the Bible, it makes for rather untenable doctrine. All Souls’ Day, in Roman reckoning, is a special day to pray for the souls in purgatory; it’s a neat complement to All Saints Day, celebrating the souls now fully glorified in heaven.
Indeed, there is a neat three-fold structure of the church that they put forth: the church militant (us on earth, still fighting sin), the church expectant (in purgatory, awaiting full release), and the church triumphant (in heaven, at rest). But the Scriptures don’t permit us to make a full distinction between the last two. The dead are both at rest with Christ and awaiting their resurrection unto glory. (The tension between these two realities plays heavily into divergent traditional & modern approaches to the Burial service.)
On those grounds we can still have All Saints’ Day (to emphasize their glorious rest) and Commemoration of the Faithful Departed (to emphasize their yet-unfinished story). Indeed, it is the recommendation of this Customary to treat this day as if it were a major feast day, using Occasional Prayer #113 as the Collect of the Day:
O eternal Lord God, you hold all souls in life: Shed forth upon your whole Church in Paradise and on earth the bright beams of your light and heavenly comfort; and grant that we, following the good examples of those who have loved and served you here and are now at rest, may enter with them into the fullness of your unending joy; through Jesus Christ our Lord.
If you still want to nickname it “All Souls’ Day” that’s fine… the phrase is in that collect after all. But it’s best to think of it as a complement to All Saints’ Day, considering the faithful departed from a slightly different angle.