Explain why Browning waits until the end of "My Last Duchess" to tell to whom he has been talking and why?

Browning's poem "My Last Duchess" is a dramatic monologue
that begins in the middle of a conversation between the duke and another individual.  
We can gather from the beginning that the speaker is looking at and discussing with
another the picture of his late wife

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That's my last duchess painted on the
wall,

Looking as if she were
alive

 This
situation immediately provokes questions from the reader:  What happened to the
Duchess?  What caused her death? As the speaker continues to give details about the
painting, details about her personality are also revealed to us.  We learn that she was
lively, humble, joyous, kind, and responsive to others.  Sympathy for this young woman
who died is aroused. 

But we also detect hostility in the
speaker's voice.  He is criticizing his late wife for what seems to be innocent
behavior.  He seems proud and overbearing, demanding respect for his
"nine-hundred-years-old name."  He seems to be possessive and jealous if she found
pleasure in people or things apart from him. 

Then,
the hammer falls!  We gather with shock that the Duke had had his wife killed because
she did not please him:

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This grew: I gave
commands;

Than all smiles stopped
together. 

Here the reader is
fully engaged in the text.  We want to know why the Duke is revealing such a horrendous
act and for what purpose.  The final lines seal our verdict of the Duke.  We see that
the story of his last wife was deliberately told and calculated as a warning to the
emissary of his betrothed's family as to how his new bride should act.  The ending is
chilling.  The Duke, because of his wealth and name, was able to murder with impunity,
and his new bride will have no choice but to conform to his tyranny.  The details of the
poem are arranged to provoke curiosity, create suspense, and convey a lasting impression
of a powerful man in a patriarchal society.