I wish to know the computer name associated with a known ip-address. The DNS is managed by my router (WIND3 webcube) and I can see the resolved name using the browser (http://192.168.1.1) Nevertheless, I wish to read the LAN computer names by command line from the console. I've tried <ping -r 192.168.1.255> then <arp -a> as suggested by Bodo; this has shown all IPs & relevant MACs on the LAN except my own; the only hostname shown has been the router name corresponding to 192.168.1.1 - half question has been answered, now I have a way to discover remote IPs on the LAN by console. In addition, using <nmap -sn 192.168.1.0/24>, I can see the full list of IPs on the LAN but still no hostnmes.
At the moment the best solution is running this script:
for x in {101..110}
do nslookup 192.168.1.$x | grep name
done
that shows all active names and relevant IPs (reversed)