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...