After quick investigation I’ve found gxmessage which is available as deb package for both Debian and Ubuntu.
I installed it and use in the following way:
root@linux:~# apt-get install gxmessage
hipo@linux:~$ ssh firstname.lastname@example.org
hipo@remote-desktop:~$ DISPLAY=:0; XAUTHORITY=~owner_of:0/.Xauthority; export DISPLAY XAUTHORITY
hipo@remote-desktop:~$ gxmessage 'Heya what's up ;) Wanna have a cake?"
Below you see what pops up on the screen on the remote-desktop Gnome Desktop 😉
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Tags: cake, deb, deb package, Desktop, export, export display, Gnome, gnome desktop, gnome user, gxmessage, gxmessagehipo, investigation, Linux, package, remote desktop, remotehost, root, root linux, screen, ssh, terminal, terminal session, Ubuntu, use, way, work, Xauthority, XAUTHORITYhipo