Did the Valar make a huge mistake?

[obloquy]

I think even more important than your points, HerenIstarion, are Tolkien's own, which are quoted above as well:

Should Manwe and the Valar meet secrecy with subterfuge, treachery with falsehood, lies with more lies? If Melkor would usurp their rights, should they deny his? Can hate overcome hate? Nay, Manwe was wiser; or being ever open to Eru he did His will, which is more than wisdom. He was ever open because he had nothing to conceal, no thought that it was harmful for any to know, if they could comprehend it. Indeed Melkor knew his will without questioning it; and he knew that Manwe was bound by the commands and injunctions of Eru, and would do this or abstain from that in accordance with them, always, even knowing that Melkor would break them as it suited his purpose. Thus the merciless will ever count on mercy, and the liars make use of truth; for if mercy and truth are withheld from the cruel and the lying, they have ceased to be honoured.

Manwë was such a purely good being that he was incapable of any injustice; revoking the opportunity for Melkor to repent and be redeemed would have been unjust. Was it even within Manwë's rights to do so? Manwë and Melkor were coequal beings -- at least, neither of them were of a greater order of being with an inherent right to subject the other. Manwë's was not the ultimate will in itself; he was only a servant of that ultimate will. Melkor's place in Ëa made him answerable, not to Manwë, but to Eru himself, even if it was Manwë who expressed Eru's thoughts.

I disagree a little with your take on the significance of the name change. Melkor was never 'officially' renamed Morgoth; it's more of a nickname that stuck. Though he was no longer counted a Vala, he never ceased being Melkor, and he was still afforded the free will and rights of his station in Middle-earth.