Change the option "Login screen menu":
$ sudo nano /etc/X11/default-display-manager
For Gnome 2 , edit as:
/usr/sbin/gdm
For Gnome 3 , edit as:
/usr/sbin/gdm3
For KDE , edit as below
/usr/lib/kde4/bin/kdm
For Xfce, choose lightdm and edit as:
/usr/sbin/lightdm
or you can install xdm:
$ sudo apt-get install xdm
References:
Web: https://packages.debian.org/jessie/xdm
File: Debian -- Details of package xdm in jessie.pdf
Web: https://wiki.debian.org/Xfce
File: Xfce - Debian Wiki.pdf
Guides:
KDE
LXDE
XFCE
Gnome Shell Extensions
Gnome Desktop Icons, Themes and Cursors

Once the changes have been saved, reboot the computer to make run the new Display Manager and find your new "Login screen menu".

You can change more things on the menu, such as the background and colors, but depends on every Display Manager where to put what to show in the system.

Change the option 'System Default' in the login screen menu:
$ sudo update-alternatives --get-selections
$ sudo update-alternatives --config x-session-manager
And then choose an option

References:
Web: http://superuser.com/questions/376107/how-change-the-default-desktop-manager-in-debian
File: linux - How change the default desktop manager in debian_ - Super User.pdf

Slim:
Is a desktop-independent graphical login manager for X11.
Web: https://packages.debian.org/jessie/x11/slim
File: Debian -- Details of package slim in jessie.pdf

Change the login background: 
Web: http://www.linuxquestions.org/questions/debian-26/changing-the-login-screen-background-in-debian-wheezy-lxde-4175446494/
File: Changing The Login Screen Background in Debian Wheezy(LXDE)_.pdf

Add new input sources (keyboard or keyboard configuration (layout)) to the login screen:
References:
Topic: Look for the section Keyboard
Guide:
Set Keyboard, Region and Language

Note:
Sometimes, when someone changes the "x-session manager" it is impossible to return to a previous Desktops Environment used. That could happens after a log out or even after a reboot or a power off. To resolve that problem we can try these alternatives:
1. Change the current x-session manager, using the current guide, and then try to log in the environment again.
2. Identify the running x-session manager service, and then stop and start the service, using a command like in the next example:
Identify the x-session manager version:
$ sudo dpkg -l | grep 'gdm'
Output:
ii  gdm3                                                             3.22.3-3+deb9u1                             amd64        GNOME Display Manager
ii  gir1.2-gdm-1.0                                                   3.22.3-3+deb9u1                             amd64        GObject introspection data for the GNOME Display Manager
ii  libgdm1                                                          3.22.3-3+deb9u1 
End of output.
Identify the status of the service and then restart it or stop it and start it (Systemd services):
Display the services list, in order to identify the x-session manager:
$ sudo systemd
Display the status, attempt to restart the service, or finally stop it and restart it:
$ sudo systemd status gdm.service
$ sudo systemd restart gdm.service
$ sudo systemd stop gdm.service
$ sudo systemd start gdm.service
3. If the last alternatives don't resolve the issue, reboot the computer and that is going to work.
4. If nothing works as well, you can always un-install re-install any of your x-session managers.

