Pinning Edge on taskbar for each different profile makes some not display the profile name

The original issue was root caused. If you close and reopen Edge, the name updates but it doesn't update in realtime. Considering this easy workaround, we are currently not planning to fix this since most customers close and reopen Edge pretty often. 

Gordan Redzic - regarding the issue you mentioned, there is another pesky bug you could be hitting which causes the default profile not to be badged. It is fixed in the latest Canary version. To workaround this issue in the meantime which this fix rolls to dev, beta and stable, you can use the below instructions. 

1. Open your broken shortcut, by right clicking on the taskbar icon, then right clicking on "Microsoft Edge" in the jumplist and opening "properties"
2. Update the target string to be appended with: --profile-directory=”Default”
3. Click “Change Icon”, Click “Browse”, in the “File name” field at the bottom of the explorer window enter:

“%localappdata%\Microsoft\Edge SxS\User Data\Default\Edge Profile.ico” (without quotes 😊)

Select the Edge icon that is badged with your profile image, in the change icon dialog.

4. Click apply to correct the shortcut’s properties.