In the simplest possible terms, the theme of Christina Rossetti's poem, "When I am dead, my dearest," is death. The speaker is in a melancholy mood, contemplating the prospect of dying. She asks that her "dearest," presumably her lover, not mourn for her.
Perhaps it might be more accurate to say, however, that the poem is about mourning, the necessity of mourning, and why we mourn. Rossetti's speaker is keen to emphasize the fact that mourning is not for the dead person but for the person who survives them. It does not matter to the dead person whether the beloved chooses to "remember" or "forget" because the dead person will not be there to witness what is going on in his or her absence.
The second stanza of the poem makes this very clear. Rossetti repeats the phrase "I shall not" at the start of three successive lines to emphasize the fact that the dead person is insensate to what is happening above their grave. Rossetti does not claim to know what the dead person will feel—they, like the mourner, may either "remember" or "forget." What happens, however, will not depend on the behavior of the mourner.
Ultimately, Rossetti's poem seems to convey the message that we must all choose to mourn in our own ways, rather than thinking about what the person we are mourning would prefer. This is because mourning is really about the living, not about the dead.