Is it possible to configure OS X to use the domain-name supplied by DHCP option 15?
Not understanding whats exactly your problem. Maybe this can help you.
If you set the search option, in your own config (network->advanced->dns->search domains) or by your dhcp server. You basically eliminate the need to add this part to a fqdn.
Example:
search: foo.com
then,
ping test
would try to resolve test.foo.com
So, in your case that would be test.my.example.com
Futhermore, setting your local name, you can change under:
Sharing -> Edit...