I would say that Donne uses this title because it sums up the point that the speaker is trying to make. It is telling the speaker's love that, although they are parting, there is no reason for sorrow because they will not truly be apart.
A valediction is a parting statement, something you say to someone as you and they are leaving one another, a farewell. So this makes sense as a title because the lovers are being separated.
But in this poem, the speaker is saying that the two of them will not really be separated because their love will keep them in touch. Therefore, the speaker is telling his love not to be sad -- he is forbidding mourning.
The term "valediction" means "farewell". Thus this is a "goodbye" poem in which a lover is leaving his beloved. The departure can represent both a temporary one of the separation of living lovers but also represent the ultimate form of departure which is death.
Similarly to Donne's other poem on the same theme, "Sweetest love, I do not go", this poem suggests that true lovers should not mourn either temporary separation or the death of the beloved. The reason for "forbidding mourning" upon separation is religious.
The Reverend John Donne was a priest in the Church of England. That means that he was a dualist who believed that mind and soul were independent of the body and that the soul persisted after death. From a religious viewpoint, there are two types of love, a carnal sublunary kind (focused on "eyes, lips, and hands") and a spiritual kind. Spiritual love rather than being thwarted by absence of a lover's physical self becomes stronger, because in the absence of the physical, what remains is "so much refined" as to be purely spiritual.
Although “valediction” now suggests the valedictory addresses familiar at high school and college graduations, in this poem the word is to be taken literally, as the saying of a farewell. The speaker is speaking to his lady, to whom he is married or affianced, and who has apparently been “mourning” at the prospect of his departure. The poem is developed as a set of statements and arguments to deflect the listener’s crying and mourning. A trip at this time, would have been greatly lengthy and taken a long time, and could possibly have been a difficult trip and also one that might have been incredibly arduous.