I can't find a way to remove weekday name from clock applet in gnome-shell, is it possible without editing the source?
Two answers to your original question:
For Unity, choosing 'Ubuntu' at the login screen you can do it:
For Gnome 3, choosing 'Gnome' at the login screen you cannot do it:
The setting does not exist as the screenshot shows below.
Best bet may be a Gnome 3 extension, or a bug report.
If you're using GNOME 3.x then you can adjust clock setting using
You can also look in g-settings via a terminal:
which gives only two options:
I case you've missed it in comments, here are two patches:
However, they need a verification on the latest version of GNOME since I'm no longer using it.