…or rather the name ;)
I bet that if you wake up most “identity professionals” in the middle of the night and ask them what an identity token is, the answer would be “a token about the identity of the user”.
This is not wrong – but it is definitely not the rightest answer.
In OIDC, the token service needs to send data about “what happened during authentication” back to the client applications, e.g. authentication method, authentication time, some protocol information and a unique identifier for the user that was authenticated. And – yes this might also include other identity information about the user, but this is optional.
This data must be sent in a format that is both tamper proof and that allows the client to authenticate the issuer. In OIDC this format is JSON – and the way how you add the above security properties to a JSON object is by wrapping it in a JWT (along with JWS, JWA and JWK) – hence the name identity token. I would prefer “authentication response” instead – because that’s exactly what it is.
Also, some people are confused and think you can also use the identity token to act like an “access token”, which is wrong. Not using the word “token” at all, would be much clearer.