The original system username is not written unless you use something like this answer - i.e. click the username as part of the connection. The remote host is encoded in the SSH_CLIENT environment variable, so it can be defined.
You can try the remote finger system, but that requires fingerd , which is currently not a regular service.
You will be able to use certain keys for users, which may have parameters set at the beginning of the key, such as environment="NAME=value" in the authorized_keys file, to determine how the remote user connects. eg.
environment="REMOTEUSER=fred" ssh-rsa <blahblahkey> <comment>
Using the environment parameter in the key will work only if you set PermitUserEnvironment to the sshd configuration, otherwise the line in authorized_keys will be ignored and you will be asked to enter the password.
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