I went through all this with my G27 and Win10 and it being recognized as Driving Force GT... It is annoying to say the least. I had varied success with varied fixes. Some didn't work at all, some would but the it'd be back to Driving Force GT recognizing the next boot up, some even seemed like they'd work for a week or something only to fail again. So in the end I combined all the convoluted steps of the ones that made the most sense or showed the best results.

It is a long mess, and it is probably just one thing in all this that is actually doing the work, but after doing all this my wheel has been working properly for months with no hiccups. Like I said, probably ten steps too many, but it worked for me so I'll share;

First you wanna remove all signs of the bad install;

1. I unplugged everything and uninstalled the Logitech Profiler software.
2. I ran WheelDriverCleaner.exe from Logitech. http://chilp.it/c09316a
3. I followed these steps about removing listings from the device manager. A lot of Logitech moderators will always recommend these steps on their official forums when you see people posting about this issue.
"

    Launch command prompt (Start menu > type cmd in the search box). Command box will appear.

    Type this command: set devmgr_show_nonpresent_devices=1. (This will make sure all entries show in the Device Manager of Windows)

    Then, run the command devmgmt.msc to start Device Manager from the Command Prompt or open it how you see fit.

    Once the Device Manager is open, click on the menu item 'View', then 'Show Hidden Devices'.

    In the main window click to expand the categories "Human Interface Device" and "Universal Serial Bus Controllers".

    You will see sub-entries with lighter, transparent icons. These are called "ghosted devices". Select and delete all of those entries. Just do it one at a time. (Right click > uninstall or highlight and press delete)

    Restart the computer

"

Then I followed these steps when reinstalling the Logitech Software that some guy posted on the Logitech forums;

"

    Download lgs510_x64.exe (I use the one that comes from the Logitech Website. I guess for awhile they didn't have the x64 version on their website for some reason. So people started uploading copies places. But, there is one on the Logitech site last I checked, so its the one I feel safest using; http://www.logitech.com/pub/techsupport/joystick/lgs510_x64.exe )

    Open it. But don't click anything after opening it!

    Open the path C:\Users\"YourUserName"\AppData\Local\Temp\

    Do a search with CTRL+F and find the folder named 2b-LGS-x64
    Open the most recent folder named 2b-LGS-x64 and navigate to \Common64\Logitech\WMDrivers\
    Right-click on wmjoyhid.inf and choose Install. It'll happen instantly.
    Now, go back to the Logitech install window you left open and install like normal and plug in your wheel when it tells you to. (A big tip here; I have seen users and moderators recommend using a USB 2.0 slot rather than a USB 3.0 slot if possible when plugging in your wheel! Also, always using the same USB slot each time you use your wheel is recommend)
    Restart your PC

"
Should show up as the G27 in Logitech Profiler from now on!

Then make sure you make your game specific Logitech Profiler profile for Automobilista with the Reiza recommended settings.

Check 'Use Special Force Feedback Device Settings'
Overall 100%
Spring 0%
Damper 0%
Check 'Enable Centering Spring'
Center 10%
Uncheck 'Use Special Steering Wheel Settings'
Check 'Use Special Game Settings'
Check 'Allow Game To Adjust Settings'

Should be good to go. Its a ton of trouble but it worked for me. After how much stuff I tried I'd say it was worth it. But I of course cannot guarantee anything here. I've shared it with a few people that never followed up so could be nothing more than a shot in the dark. Good luck!