Answer nº 1 -
su -
xhost +si:localuser:gdm
sudo -u gdm gnome-control-center
Answer nº2 - You can change the GDM screen background through the console.
su -
su - gdm -s /bin/bash
dbus-launch | sed "s/^/export /"
GSETTINGS_BACKEND=dconf gsettings set org.gnome.desktop.background picture-uri "file:///usr/share/backgrounds/FILE.JPG"
Where "FILE.JPG" with the picture you want to use as the GDM3 login screen background.
Please note that you must specify a file which user "gdm" has permission to read, that's why I've used file:///usr/share/backgrounds/. For instance, user "gdm" cannot read files in your home directory.
In the same way you can also change the GNOME 3 login screen GTK theme (first 3 commands are the same):
su -
su - gdm -s /bin/bash
dbus-launch | sed "s/^/export /"
GSETTINGSBACKEND=dconf gsettings set org.gnome.desktop.interface gtk-theme "THEMENAME"
Where "THEME_NAME" is the name of the theme, e.g.: "Zukitwo". The themes must be placed under /usr/share/themes/.
Source of article
Answer nº 3 - just change the picture in /usr/share/backgrounds/beefy-miracle/default/wide/beefy-miracle.png
Answer nº4 - You can also try a graphical tool called GDM3setup
Answer nº 5 - Edit the file /usr/share/backgrounds/spherical-cow/default/spherical-cow.xml
Change the file /usr/share/backgrounds/spherical-cow/default/wide/spherical-cow.png to whatever you want.