The first 4 stanzas are Emily describing the process of death as an observer, but the final 4 stanzas could be describing how the dead “rejoin its own” or how we, the survivors “rejoin” our own after we are parted from the dead and as we go on about our lives. She could also be saying that she’s giving herself “permission” to let the dead go, or that God / “Death” has given the dying “permission” to enter the next life.
The first line of the poem begins with the beginning of the end of life as the subject finds themselves in the spasm of death. There entirety of the life of this person comes before the first line of the poem and their mortal existence ceases in the line break between stanzas. We do not know who this person is – Emily does not describe her feelings for the subject and if she lived them, cared for them, or even knew them. In fact the suddenness in which the poem begins with the spasms of death almost feels as if Emily has stumbled upon this scene, perhaps the way one would when they see the image in a newspaper of a soldier who has died on the battlefield – death is thrust upon is suddenly and we recognize it, even if we don not recognize the person who has died.
Lines 2-4 deal with “breath” in that “An extasy of parting” isn’t just the soul “parting” the body, it’s also the breath “parting” the mouth. This is supported by her use of the word “Denominated” which means “to give a name or appellation to; to call by a name” (OED) and is also a play on the word ‘dominated’, thus the name if death dominates the final breath of the subject.
Emily continues this naming of “Death” with her use of the word “mention” at the beginning of the second stanza. This “anguish” is not only felt by the observer (be it we the reader or Emily) in regard to whom is dying, but it could also refer to the subject themselves who is in “anguish” as they speak the name of “Death” who has complete control over them (dominates them). Her use of the word “grown” is a play on “groan” which could be the only way a person could pronounce the name of death and recalls the “throe” (spasm) of the first line. And perhaps this naming of “Death” is what allows for “permission” to be given for the subject to “rejoin its own” (the other dead) which mirrors the observer who must, with “patience”, allow the person to “rejoin [their] own” by moving on with their own life. In death the dying and the living must both move on with their own kind.