In another forum i’ve found the cc3000 is capable of netbios and mDNS.
I just checked in (http://cc3000.codeplex.com) local name resolution that appears to work! I went through a few options, mDNS, LLMNR, DHCP Inform, and NetBIOS Naming. I really wanted LLMNR to work, but despite the cc3000 sending what looked like perfect responses, the clients never seemed to accept the name. The DHCP Inform, just didn't work, I think you have to specify hostname in the initial DHCP negotiation with the router and I don't have that level of control with the cc3000. So, I ended up, unbelievably, with the oldest method... NetBIOS Naming. It just plain works... The mDNS worked almost immediately. So with those 2 working and a web server running, I have now run for 24 hours! The image is what my testing looks like. That's my development machine (windows 8.1), an iPad 2, and a Surface RT. All of which are happily resolving the name "cc3000.local". Now, you might ask, what about my Android!? Well, I have a Nexus 7 for testing of that platform as well, but guess what... Android does not support any local name resolution. So, there is nothing you can do to make it work, other than setting the hostname through DHCP and letting the router answer the DNS request, but as I mentioned, I don't have that level of control on the cc3000. I have suggested the change to TI, with no response.