I tried disabling the motd.dynamic in /var/run renaming the file, but did not work because the system recreates the file.
Does anyone know disable it?
The script files in
/etc/update-motd.d generate the file
/var/run/motd.dynamic which you've identified as containing your MOTD.
A simplistic way to stop generating this file would be to make all of the scripts non-executable with:
chmod -x /etc/update-motd.d/*
Note: Information taken from this answer by heemayl.