The greeter logo on the login screen is controlled by the org.gnome.login-screen.logo GSettings key. Since GDM uses its own dconf profile, you can add a greeter logo by changing the settings in that profile.
When choosing an appropriate picture for the logo to your login screen, consider the following picture requirements:
All the major formats are supported: ANI, BPM, GIF, ICNS, ICO, JPEG, JPEG 2000, PCX, PNM, PBM, PGM, PPM, GTIFF, RAS, TGA, TIFF, XBM, WBMP, XPM, and SVG.
The size of the picture scales proportionally to the height of 48 pixels. So, if you set the logo to 1920x1080, for example, it changes into an 85x48 thumbnail of the original picture.
Create the gdm profile which contains the following lines:
user-db:user system-db:gdm file-db:/usr/share/gdm/greeter-dconf-defaults
gdm is the name of a dconf database.
Create a gdm database for machine-wide settings in /etc/dconf/db/gdm.d/01-logo:
Replace /usr/share/pixmaps/logo/greeter-logo.png with the path to the image file you want to use as the greeter logo.
Update the system databases:
# dconf update
Make sure that you have run the dconf update command to update the system databases.
In case the logo does not update, try restarting GDM.
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