This paper investigates __anonymity__ of all NIST PQC Round~3 KEMs: Classic McEliece, Kyber, NTRU, Saber, BIKE, FrodoKEM, HQC, NTRU Prime (Streamlined NTRU Prime and NTRU LPRime), and SIKE.
We show the following results:

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* NTRU is anonymous in the quantum random oracle model (QROM) if the underlying deterministic PKE is strongly disjoint-simulatable. NTRU is collision-free in the QROM. A hybrid PKE scheme constructed from NTRU as KEM and appropriate DEM is anonymous and robust. Similar results hold for BIKE, FrodoKEM, HQC, NTRU LPRime, and SIKE.

* Classic McEliece is anonymous in the QROM if the underlying PKE is strongly disjoint-simulatable and a hybrid PKE scheme constructed from it as KEM and appropriate DEM is anonymous.

* Streamlined NTRU Prime has an obstacle for the IND-CCA security proof as Grubbs, Maram, and Paterson pointed out that Kyber and Saber has a gap in the current IND-CCA security proof (Cryptography ePrint Archive 2021/708).

Those answer the open problem to investigate the anonymity and robustness of NIST PQC Round~3 KEMs posed by Grubbs, Maram, and Paterson (Cryptography ePrint Archive 2021/708).

We use strong disjoint-simulatability of the underlying PKE of KEM and strong pseudorandomness and smoothness of KEMs, which will be of independent interest.

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