bah muhr-e nāmah jo bosah gul-e payām rahā
hamārā kām huʾā aur tumhārā nām rahā
1) since on the seal of the letter, the kiss remained the rose/'flower' of the message
2) our desire/work occurred, and your fame/name remained
nām : 'Name, appellation, designation, title; — good name, repute, reputation, character, fame, honour, renown'. (Platts p.1118)
gul-e payām = one meaning of gul is 'result' and 'benefit'; and another meaning is 'better' and 'fine'. [An illustrative verse by Urfi.]
In Ghalib's verse the meaning of gul-e payām can be 'result' of the message. But better than this is 'fine' and 'better'-- that is, the best part of the message. The beloved has applied to the letter a seal with her name, and sent it off. The lover has kissed the seal, and this proved to be the best part of the message. From kissing your seal our desire/work occurred-- that is, the goal was attained; and your name/fame occurred [his text has huʾā instead of rahā], that you treated your lover affectionately. When only/emphatically kissing the seal is the best part of the letter, then it's evident that the letter will surely be despair-creating.
For more on Ghalib's unpublished verses, see the discussion in {4,8x}. See also the overview index.
The question of what exactly gul-e means has been discussed extensively in {71,1}, with regard to its lovely gul-e naġhmah .
This verse has nice punchy sound effects: consider nāmah , payām , kām , nām , and also rahā , hamārā , tumhārā , rahā . That second line, with its two symmetrical halves and air of triumphant efficiency, is also a treat-- and an immediate source of suspicion, since a claim of 'triumphant efficiency' from the lover is so unlikely to be true.
The beloved's imagined 'kiss' on the paper before sealing it has two advantages: the lover's 'desire/work' is accomplished (because he gets to touch and kiss the romantically endowed seal-imprint), and the beloved's 'name' remains (because the imprint of her seal has penetrated more deeply into the lip-moistened paper). Or else, of course, her 'name' and fame remained, since despite the lover's (show of) satisfaction, we know in our hearts that the letter itself no doubt upholds her reputation as a notoriously cruel and tyrannical beloved.
Zamin:
[A discussion of how and why some manuscript evidence exists for a refrain of huʾā rather than rahā for this verse.]
Often at the time of impressing a seal, people apply their lips to the paper, so that from that moisture the print of the seal would emerge clearly. The poet assumes that when the beloved impressed the seal on the letter, then she applied her lips. Then, having imagined this action to be a kiss, he fancies that in this embellishment she has sent him the 'message of a kiss'; bosah bah paiġhām is an idiom.
How can this free, imagined happiness be expressed?! He is absorbed in it: our desire/work happened, and your name occurr ed. Look at this very same theme in {248x,3}:
misī-ālūdah hai muhr-e navāzish-nāmah z̤āhir hai
kih dāġh-e ārzū-e bosah detā hai payām us kā
[missi-stained is the seal of the caressing letter; it's evident
that the wound/scar of the longing for a kiss gives its message]
== Zamin, p. 112