I can identify Windows' Releases very easily even after the login process is over.
Ubuntu's Desktops are similar between releases.
Is it possible to identify the release by looking at Ubuntu's Default wallpaper / Desktop?
If you want a GUI mode to check the release version, just launch the System Monitor, the answer is on the system tab.
An alternate way is to guess by the default wallpaper, every version has a different, although similar looking wallpaper. Look here
Reflecting the comment What if they don't use the default wallpapers?: Because Linux/Ubuntu is very, customizable the users can easily change their whole Desktop Environment, so in that case it is impossible to tell by appearance. (Note: This is same with windows, the whole shell can be changed there also, and after that you won't be able to tell the difference. The difference is that on windows this is hard to do, and only the powerusers/customziers do this. So it is unusal to see a win computer with a non-default shell, on linux it is usual.)
This might be impossible in the case of most previous Versions, especially from a customized desktop. It can be made possible in next versions by making slight changes in the bar on the desktop. So, an expecting solution is:
Add the Version to the name -- 'Ubuntu Desktop', that we see on the left top corner. Add one star for a version released just after an LTS version...two stars for the next......four stars for the LTS.
Keep a minimum space to show at least Ubuntu's logo and the Version to give freedom (to the user) to add more icons on this bar upto a certain limit without losing the identity.
Use an entirely different Default wallpaper for each LTS version.
It will be useful if the Code name of LTS version is also added in the Log-in screen (not on the bar). No need of Code name in Non-LTS