It didn't work, because the SFTP server farm appears to the client as one server. With your SFTP client you connect to the farm and the rest is business of the farm. So even if you might be assigned to one of the servers that form the farm, the SFTP still returns the name of the whole farm, because it doesn't know anything else.
So the SFTP protocol itself cannot help you, but SFTP runs over SSH, which could do what you want.
One soulution that might work is to run command on the server you are connected to. (If the server allows it, of course.) You can use the
SftpCommandRunner helper class.
A sample of use:
Sftp client = new Sftp();
string hostname = SftpCommandRunner.RunCommand(client, "hostname -f");
string ipaddress = SftpCommandRunner.RunCommand(client, "hostname -i");
However, the commands are definitely OS dependant. The example would work on servers with unix systems on it.
By the way, why do you want to do it at all?