My home computer is connected directly through a modem to my ISP. How can I prevent my IP to return a host name when I use this website ?
so... I take it that the request goes directly to my ISP and not to my computer ?
Unless you have full control of the netblock you're in (which you don't), the only thing you can do is ask your ISP to remove the PTR record for your IP (which I doubt they'll agree to do).
Also, there's nothing special about that website. It's just a front-end to dig, host, nslookup, etc.
Regarding your edit, that's correct. The DNS request goes to the authoritative servers for your netblock, which in most cases, are run by your ISP.
You can't. This is a DNS entry that is owned by your provider. You could ask them to change it for you, but you probably won't get far - especially since your IP is probably changing every time you connect.