Hi,
I'm going to install your IP update client on a Linux Ubuntu server and I will run the command:

systemctl start dynuiuc.service

After a server reboot does the service automatic restart?
Thank you

I answer myself: No, it does not.
After a server reboot If I write the command:

systemctl status dynuiuc.service

this is the answer:

dynuiuc.service - Dynu IP update client daemon
Loaded: loaded (/usr/lib/systemd/system/dynuiuc.service; disabled; vendor pre
Active: inactive (dead)

I've found this solution, write the command:

systemctl enable dynuiuc.service

and then the command:

systemctl start dynuiuc.service

last find the file:

/usr/lib/systemd/system/dynuiuc.service

and edit the line:

--pid_file /var/run/dynuiuc.pid
change it to:

--pid_file /run/dynuiuc.pid
Regards
Enrico