"When I am dead, my dearest" is divided into two stanzas. In the first stanza, the speaker tells her loved one(s) not to mourn her death. 

This first stanza sounds selfless and it very well may be, but in the second stanza, the speaker detaches herself from her would-be mourners by saying that she will not be present to experience suffering. Therefore, it would be useless to mourn her and useless for her to mourn her own death since she will be free from the suffering of life: 

I shall not see the shadows, 
I shall not feel the rain; 
I shall not hear the nightingale
Sing on, as if in pain: 

The speaker seems to make it easier for her mourner(s) and herself when her death does come. But at the end of each stanza, she does not commit either to this selfless ("Sing no sad songs for me") implication nor to the indifferent attitude in the second stanza where she states that she will not be there (alive) to notice what she is missing (good or bad). The speaker absolutely does not commit to a singular statement and this is shown in the last two lines of each stanza. Remember me if you want to and I might remember if I am so inclined. 

This reveals an uneasiness and uncertainty in the poet's (or speaker's) mind. She wants her death to be painless for her "dearest" and for herself. She rationalizes that her dearest should live ("Be the green grass") rather than mourn the dead and she rationalizes that when she dies, she will have no need of earthly memory or of being remembered. But then again, she hesitates and adds the possibility that she might like to be remembered and that she might like to remember herself (perhaps in the afterlife). In trying to make sense of death, the speaker rationalizes but can not commit to forgetfulness completely, probably because she is not clear what death really will be like. 

It has been argued that Rossetti had expected to die young and some of her poetry has been motivated by self-pity. In that respect, this poem is a kind of veiled self-pity where she wants her dearest not to mourn but leaves the question undecided about whether or not she would like to be remembered. The poem is also about the speaker's uncertainty about death. Is death/afterlife a realm in which she would want to remember or be remembered? Is it a realm of forgetfulness? This uncertainty might reflect that the speaker is someone who is generous but a little vain, someone who is religious but also has doubts.