diff --git a/src/core/execute.c b/src/core/execute.c
index b485509bdf5..5a2c095e857 100644
--- a/src/core/execute.c
+++ b/src/core/execute.c
@@ -321,6 +321,7 @@ static int connect_journal_socket(int fd, uid_t uid, gid_t gid) {
 static int connect_logger_as(
                 Unit *unit,
                 const ExecContext *context,
+                const ExecParameters *params,
                 ExecOutput output,
                 const char *ident,
                 int nfd,
@@ -330,6 +331,7 @@ static int connect_logger_as(
         int fd, r;
 
         assert(context);
+        assert(params);
         assert(output < _EXEC_OUTPUT_MAX);
         assert(ident);
         assert(nfd >= 0);
@@ -358,7 +360,7 @@ static int connect_logger_as(
                 "%i\n"
                 "%i\n",
                 context->syslog_identifier ?: ident,
-                MANAGER_IS_SYSTEM(unit->manager) ? unit->id : "",
+                params->flags & EXEC_PASS_LOG_UNIT ? unit->id : "",
                 context->syslog_priority,
                 !!context->syslog_level_prefix,
                 output == EXEC_OUTPUT_SYSLOG || output == EXEC_OUTPUT_SYSLOG_AND_CONSOLE,
@@ -572,7 +574,7 @@ static int setup_output(
         case EXEC_OUTPUT_KMSG_AND_CONSOLE:
         case EXEC_OUTPUT_JOURNAL:
         case EXEC_OUTPUT_JOURNAL_AND_CONSOLE:
-                r = connect_logger_as(unit, context, o, ident, fileno, uid, gid);
+                r = connect_logger_as(unit, context, params, o, ident, fileno, uid, gid);
                 if (r < 0) {
                         log_unit_error_errno(unit, r, "Failed to connect %s to the journal socket, ignoring: %m", fileno == STDOUT_FILENO ? "stdout" : "stderr");
                         r = open_null_as(O_WRONLY, fileno);
diff --git a/src/core/execute.h b/src/core/execute.h
index 4742f4e6c1c..8b2b80d34ea 100644
--- a/src/core/execute.h
+++ b/src/core/execute.h
@@ -259,12 +259,13 @@ typedef enum ExecFlags {
         EXEC_APPLY_CHROOT      = 1U << 1,
         EXEC_APPLY_TTY_STDIN   = 1U << 2,
         EXEC_NEW_KEYRING       = 1U << 3,
+        EXEC_PASS_LOG_UNIT     = 1U << 4, /* Whether to pass the unit name to the service's journal stream connection */
 
         /* The following are not used by execute.c, but by consumers internally */
-        EXEC_PASS_FDS          = 1U << 4,
-        EXEC_IS_CONTROL        = 1U << 5,
-        EXEC_SETENV_RESULT     = 1U << 6,
-        EXEC_SET_WATCHDOG      = 1U << 7,
+        EXEC_PASS_FDS          = 1U << 5,
+        EXEC_IS_CONTROL        = 1U << 6,
+        EXEC_SETENV_RESULT     = 1U << 7,
+        EXEC_SET_WATCHDOG      = 1U << 8,
 } ExecFlags;
 
 struct ExecParameters {
diff --git a/src/core/manager.c b/src/core/manager.c
index 7f9c6164c71..6ddaae8c91c 100644
--- a/src/core/manager.c
+++ b/src/core/manager.c
@@ -3422,6 +3422,8 @@ int manager_set_exec_params(Manager *m, ExecParameters *p) {
         p->cgroup_supported = m->cgroup_supported;
         p->prefix = m->prefix;
 
+        SET_FLAG(p->flags, EXEC_PASS_LOG_UNIT, MANAGER_IS_SYSTEM(m));
+
         return 0;
 }