My host name is updated, but I keep going to the old IP address.

Welcome to a thing called DNS caching. Changes don't propagate immediately but take effect according to the TTL. Normally for Dynamic DNS this is 60 seconds. If you're still seeing the old IP after that then this means that somewhere in your resolver chain something is caching the old value beyond the TTL.

On Windows try ipconfig /flushdns then try the ping again. On MacOSX you'll need either dscacheutil -flushcache or lookupd -flushcache for versions before 10.5.1. On Linux try restarting the name service cache daemon (/etc/init.d/nscd restart).

If after that it still doesn't change then it may mean that your ISP's DNS servers are ignoring the TTL. Your only option there is to change to another DNS provider like Internet Guide from DynDNS or OpenDNS.