"finger" shows the originating IP/domain name of the telnet session, whereas who and w only show the userid, psuedo tty and the currently running command.
This is not what I wanted. I connect from my PC, with putty, to UNIX and I run a script. Does the script can tell it's me who has logged on and launched the script, something that identifies my PC.
In fact the better for me is who am i: the name of MY remote machine is displayed.
Only problem: if I migrates with su - <USER> , we do not see it.
But actually who am i is enough ... I close the issue.