What's interesting about the beloved in this sonnet is how little we learn of her. While tradition has it that this is a poem about Anne Boleyn, the ill-fated second wife of Henry VIII, if we look solely at the text of the poem, we find it is more about the narrator than his beloved.
He is in love with an unattainable woman, who he imagines as a hind or deer he has been pursuing. A deer would be a graceful, swift-footed and elusive creature, this one especially so, but a deer is also a form of prey, a creature hunted, an object. Either you triumph over it by killing or capturing it, or it triumphs by eluding you. It is a prize whose capture becomes a display of your manhood. The beloved is a beautiful creature of nature but also a quarry to be possessed.
The narrator is obsessed with with a woman he cannot have—possibly precisely because he can't have her. He says to other men who might want to pursue her that she is out of reach for them too. We learn that her diamond collar means she is the possession of another man and a "caesar" or king at that. We also learn at the end of the sonnet that the nature of this beloved women is wild.
One way to approach the beloved in this poem is through a feminist lens. The narrator's idea of love is sexist by our modern standards. The beloved is compared to an animal, seen as a form of prey, and not given distinctive human characteristics. The narrator doesn't object to her being the property of another man: he might not like that another man owns her, but he doesn't protest the right of male ownership. What woman would have a chance with that kind of "love" surrounding her? Can we blame her for wanting to be wild?