I am operating with multiple profiles at the same time. Thunderbird is running multiple instances and I cannot see which is which.
As it is not easy to see which profile the application has opened, I suggest to add the profile alias name to the thunderbird application title being shown in the operating system launcher panel.
I found no way to change the icon depending on my instance call so this is not an option.
There is a "profile switcher" extension for windows that seems to also be able do that, but it does not work for Linux.