why the duke chose not to call his former duchess by her name?
The duke is overly proud of his heritage, and places all his self-worth in his title. The name, or, by extension, the heritage of his previous duchess is irrelevant to him. In fact, he has apparently had many duchesses, of which the portrayed one is merely the “last” or latest. The current candidate, the daughter of a count, is also unnamed, because it is her father’s “known munificence” that is being sought, not “his fair daughter’s self,” as the duke claims (to the reader, an ironic claim and one which the ambassador sees through). There is a reflection of this disdain in the last lines of the poem: “Notice Neptune, though, taming a seahorse…” since the Greek god is named but the seahorse is one of many, although “thought a rarity.” The entire dramatic monologue works on that ironic level.