FIPS 140-3 applies to cryptographic modules, not to a product name in isolation. The key-management map should therefore start with the module boundary, tested operational environment, security level, service name, and the sensitive security parameters handled by that service.
For each service, the module owner records whether the behavior is key generation, key agreement, key transport, key encapsulation, key derivation, key entry, key output, storage protection, or zeroization. The implementation owner records algorithms, strength, inputs, outputs, failure behavior, and key purpose. The assurance reviewer records the CAVP entries, CMVP certificate, Security Policy mapping, and any caveat. A single protocol or API can contain several behaviors, so the evidence should be service-level rather than marketing-level.