I have found this possibility :
Is ther is no config file of SDDM (On systems controlled by systemd
<https://wiki.archlinux.org/index.php/Systemd>, everything should work
out of the box, since SDDM defaults to using |systemd-logind| for
session management. The configuration file will therefore not be created
at package installation time), SDDM offers a command for generating a
sample configuration file with the default settings if you really want one:
# sddm --example-config > /etc/sddm.conf
After that, you can modify the config file /etc/sddm.conf :
# Default $PATH
DefaultPath=/bin:/usr/bin:/usr/local/bin
like this :
# Default $PATH
DefaultPath=/bin:/usr/bin:/usr/local/bin:/usr/games
and the path is ok after closing and opening the session
You can also modify many other option.
For information, I have found this here
:https://wiki.archlinux.org/index.php/SDDM#Theme_settings
