For the ancient services that still insist on it (ahem, I'm looking at you, IRC), this image provides an RFC 1413 IDENT server based on Alpine Linux and using gizmotronic/nullidentd. And, because it's based on Alpine, it's small. Really small.
docker run --name nullidentd -d -p 113:113/tcp gizmotronic/nullidentd
By default the service returns a random 8-character string for each request. You may override this behavior using an environment variable.
This variable will be used to return a fixed string of no more than 20 octets (characters) for each response.
Be aware that the protocol disallows ASCII NUL, LF, and CR characters. The string will be terminated at a NUL. Any LF and/or CR characters will be stripped out of the response.
Run this command:
$ docker build -t nullidentd .