There are potentially 3 documents in play: (i) the written Agreement of the parties, if any; (ii) the Judgment of
Divorce; and, (iii) the QDRO. It is not clear from your posts where the sentence, "The Participant shall not be required to name the AP as his surviving spouse before his annuity commencement date" is located.
The important issue is the intent of the parties in their written Agreement, or, if there was no written Agreement, then in the terms of the Judgment of Divorce. The QDRO is an enforcement tool designed to implement and enforce the agreement of the parties or the ruling by the court. That's the starting point. What did the parties intend, and where is that intention reflected?
The ability of the Plan to take action may depend on the type of Plan, that is, a private company plan, a Federal, State or municipal plan, or an international plan.
So get back to us with more specifics. These matter are very fact intensive.
And BTW, you need to hire a lawyer immediately so that the other party doesn't get the court to act in your best interests without you having your say.