In your environment, one Splunk server has two NICs, each There is a different FQDN. In this case, is it possible to set the certificate and private key for both NICs?
If you can, please tell me how to set it.
You need to generate a CSR with multiple DNS names as SAN. The way to do this varies depending on what tool you're using. Then you have to give this CSR to your CA guys which will generate proper certificate with many names. If you're using openssl suite for this - google for the multiple SANs CSR generation - there are plenty solutions described on the internet.
Of course when you get your cert, you have to conifgure your splunk instance using those certs as the docs say. https://docs.splunk.com/Documentation/Splunk/8.2.4/Security/AboutsecuringyourSplunkconfigurationwith...
Private key has nothing to do with what it's used for.
And yes - the certificate can be used for multiple names. It's called "SANs" - Subject Alternative Names.