diff --git a/src/basic/argv-util.c b/src/basic/argv-util.c
index b8c371ede5..6c88dcc2ee 100644
--- a/src/basic/argv-util.c
+++ b/src/basic/argv-util.c
@@ -192,6 +192,10 @@ int rename_process(const char name[]) {
                 strncpy(program_invocation_name, name, k);
                 if (l > k)
                         truncated = true;
+
+                /* Also update the short name. */
+                char *p = strrchr(program_invocation_name, '/');
+                program_invocation_short_name = p ? p + 1 : program_invocation_name;
         }
 
         /* Third step, completely replace the argv[] array the kernel maintains for us. This requires privileges, but
diff --git a/test/testsuite-04.units/logs-filtering.service b/test/testsuite-04.units/logs-filtering.service
index fc89021ca9..06210868fd 100644
--- a/test/testsuite-04.units/logs-filtering.service
+++ b/test/testsuite-04.units/logs-filtering.service
@@ -3,3 +3,4 @@ Description=Log filtering unit
 
 [Service]
 ExecStart=sh -c 'while true; do echo "Logging from the service, and ~more~"; sleep .25; done'
+SyslogLevel=notice
diff --git a/test/units/testsuite-04.sh b/test/units/testsuite-04.sh
index 2874fc778f..d10a9afbf7 100755
--- a/test/units/testsuite-04.sh
+++ b/test/units/testsuite-04.sh
@@ -199,7 +199,7 @@ function run_service_and_fetch_logs() {
     journalctl --sync
     END=$(date '+%Y-%m-%d %T.%6N')
 
-    journalctl -q -u "$UNIT" -S "$START" -U "$END" | grep -Pv "systemd\[[0-9]+\]"
+    journalctl -q -u "$UNIT" -S "$START" -U "$END" -p notice
     systemctl stop "$UNIT"
 }