To find the answer, I consulted The Companion Bible (Bullinger). It had this preface to the book of Nahum, which helps clarify the matter.
"Nahum concludes the seven pre-captivity Prophets... and corresponding
with Jonah, which also has Nineveh for its subject. Some 87 years
before, Jonah had proclaimed Jehovah's favour to Nineveh, which had
prolonged its existence till now, when Nahum's prophecy of coming
judgment was fulfilled without further delay.
Nahum is undated; but if ch.1 vs 11 refers primarily to the Rab-shakeh
of 2 Kings 18:26-28, then we have a clue of great importance, for that
speaks of the 14th year of Hezekiah, and gives us the date as 603 B.C.
The Rab-shakeh - the chief of the captains, was apparently a renegade
Jew, and a "counsellor" high in favour with the Assyrian king
(Sennacherib)... he insisted on speaking to the common people on the
wall in the Jewish language... The Rab-shakeh's words certainly show a
deadly animosity towards Jehovah; which is borne out by Nah.1:11."
So, if Nahum 1:11 speaks of the Rab-shakeh as that "wicked counsellor" who imagined evil against God, and the following verses speak of his masters, then Nineveh is the representation of that. It would then be the dynasty of Nineveh that is meant by "no more of thy name". Nineveh would become a dead thing, cast into the grave, her bonds broken and Israel released from her cruelty, "afflicted no more" by God (vs. 12).