The criticality of log messages can be, as you may find in the documentation of journald
emerg (lowest log level, only highest priority messages), alert, crit, err, warning, notice, info, debug (highest log level, also lowest priority messages)
EDITED - changed the default criticality with a lower with "the default criticality value with a higher"
You can configure the default criticality of your service and the maximum criticality value you want to see in the logs editing the unit file. So, if you configure the default criticality value with a higher value than the maximum criticality (highest priority has 0 value, debug priority has a value of 7), the messages for the starting and the ending of the service wouldn't be displayed in the logs
EDITED - Changed the level representation with numbers
[Service]
...
LogLevelMax=1
SyslogLevel=2
You should produce logs in your service with a higher priority (with a lower priority value) than LogLevelMax (see Systemd for Developers III)
EDITED - ADDED EXAMPLE
I have made a new trivial service /root/Bin/test.bash that produces logs with Level 1 (alert)
#! /bin/bash
echo "<1>Done"
I have created a new unit (/etc/systemd/system/jmr.service):
[Unit]
Description=JMR test
[Service]
ExecStart=/root/Bin/test.bash
LogLevelMax=1
SyslogLevel=2
[Install]
WantedBy=multi-user.target
After that, I reconfigure systemd and restart the service two times
# systemctl daemon-reload
# systemctl start jmr.service
# systemctl start jmr.service
I can see that the logs only show the message "Done" (nothing in between the two logs)
# journalctl -u jmr.service | tail -n 2
ago 16 19:09:10 enreda test.bash[415488]: Done
ago 16 19:11:42 enreda test.bash[415620]: Done