Is it possible to set our domain name up on a proxy. For example, if someone pings www.ourdomain.com a proxy address will return? I would like to keep our server IP hidden?
No, it's not possible. When somebody ping your server, he request DNS record. And it's a bit difficult to change
Right, it's not possible when you ping a domain name as it replies with the A record on the DNS servers.
There are various ways to trace out the IP address the website is hosted on so blocking the ICMP packets won't do any good. Infact, even if you block the ICMP packets, the very first line of the ping command will show you the IP of the domain it is resolving to, so blocking of ping is not the solution here...