With tomorrow’s Anniversary Update for Windows 10, Cortana becomes the Windows-Internal search engine with Online access, regardless if you want it or not.
Getting rid of Cortana
You can still disable Cortana by fiddling around in the registry
Machine global: HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\Windows Search Only for current user: HKEY_CURRENT_USER\SOFTWARE\Policies\Microsoft\Windows\Windows Search
In both cases, set the value to
I’ve not yet tried it, since I’m still waiting for the Update. In case you don’t want to mess up with the registry, you can download the Regkey-Files from the article page.