OK, it isn't quite that simple to get Microsoft's new Windows 10 voice assistant to dump the Bing search engine and switch to the more familiar Google search. But it can be done. Here's how.
When you first set up Windows 10, or later in the Settings menus, you can set your default web browser. Microsoft's new Edge browser is the initial default in Windows 10 if you accepted the Express Settings during setup (which most do). But you can change your default browser back to Chrome or Firefox (or even IE) if you wish.
When you do that, search queries launched by voice input into Cortana that cannot be immediate answered will open your selected default browser, whether it be Edge, Chrome, Firefox, or IE. But you will go to the Bing search page, even in Google's Chrome browser. In other words Cortana will honor your default browser choice, but not your default search engine choice.
There is nothing inherently wrong with Bing. But I am used to Google's search and prefer it to Bing. As a longtime Chrome user (I really wish Chrome were not such a resource and battery hog on my portable machines), Google search is my natural choice.
If like me, you are a Chrome user, there is a Chrome extension (add-in program) called Chromnetana that wiill redirect Cortana from Bing to your choice of search engines, including Google. You can also pick privacy oriented DuckDuckGo or old school Yahoo.
I enjoy using Cortana in Windows 10. On my desktop PC (where battery drain is not an issue), I set Cortana to stay awake and listen for the "Hey Contana" command. It works well with my better than average Blue Snowflake desktop mic that sits between my keyboard and monitor. I can use my voice to trigger searches, launch programs, ask questions, and more.
For a list of useful ways you can use Cortana, check out this handy list from How-To Geek.