Thanks for the killall-warning. I tried the different commands in the terminal.
systemctl kill -s HUP rsyslog.service 2 lines with HUP-notice are shown in syslog. systemctl kill -s HUP --kill-who=main rsyslog.service 2 lines with HUP-notice are shown in syslog. pkill -HUP rsyslogd 4 lines with HUP-notice are shown in syslog. There is 1 main process and 3 childs.