I needed a clearer explanation than above...and specific to Windows 10 this still holds.
Disable network adapter in network settings.
Uninstall driver for that network interface in device manager.
Do not check for hardware yet.
Run Regedit as administrator.
Navigate to:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\NetworkList\Profiles
Check to see inside each folder you will find an entry that references those autosequenced network numbers.... Network, Network 2, Network 3 etc. Delete all these folders under this branch. Once you have removed all...
Navigate to:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\NetworkList\Signatures
and delete all the entries in the Managed and Unmanaged folders, but leave the two empty folders.
Go back to device manager and scan for hardware changes. Driver should reinstall automatically, and assuming your adapter is set to either obtain IP automatically via DHCP or assign itself a static IP you already know will work properly, you should get a prompt on the right of how you want discoverability for the new "Network" connection with no annoying number.
The internet was almost no help to me on this one...so if it helped you, I'm happy my intense digging through registry was worth something to someone besides just me.