This is still happening with 4.4.6-4 in Debian bookworm I used $DAEMON instead of $NAME to be consistent with the invocation in the reload function.
Besides slow restarts, this also breaks persistent data in Nagios, as it either saves that data on shutdown (which it does not a chance to do since it ends up SIGKILL'd after the start-stop-daemon call fails due to missing name), or every X minutes. The only workaround to the persistent data is to ask nagios to save it every minute, which is not great. Is there any blocker to deploying this patch or did this somehow regress? Thanks!