I guess the poet is offering up
For months they agonized over and crafted it, this gift to me they bestowed
Parents often wrestle over what name to give their child, and have - well - up to 9 months to finalize that decision, usually.
It is precious to me, not something that could ever be bought or sold
A name is yours, not something that can be bought or sold, and is (literally) who you are.
Forever mine from that day, it can never be taken from me, only given away.
You can give someone your name (by telling them what your name is). Also, in many cultures people traditionally give their spouse their name, or give up their name, at their marriage.
Yet I wanted more, and less, and so with time I crafted more in it's mold.
Children take their parents' surname - so their name is both more, and less, than their parents' but is in the same "mold".
I share my gift readily with those who's friendship is my goal
You tell your name to someone you want to be friends with.
And in truth they would be shown to use it more readily then I in any poll
You don't say your own name that often, compared to others saying your name.
Even if It were something I wished to shield it's a thing others have the right to wield
You can't really stop people from referring to you by name, even if it's to bad-mouth you.
It's forever mine, yet others claim equal ownership over it, in part and in whole
It's your name, but others may have the same name (in whole), and certainly others will have your surname (in part).
I offer you part of this gift again, but this time different from the past
The poet may be proposing, thus offering up part of their name to their intended,
I offer more, by offering less, a meager part of the whole, just the tiny bit that is last
... offering their last name,
A fraction of this thing I don't solely own, so little a thing anyone could clone
... the surname they share with their family but which is not something anyone can protect others from adopting.
Yet this meager offering more sacred to me then any riches I have amassed
The offering is of marriage, a precious thing - to share the poet's life intimately.