diff --git a/sentry_sdk/crons/decorator.py b/sentry_sdk/crons/decorator.py
index b13d350e15..fd4677709d 100644
--- a/sentry_sdk/crons/decorator.py
+++ b/sentry_sdk/crons/decorator.py
@@ -126,6 +126,7 @@ async def inner(*args: "P.args", **kwargs: "P.kwargs") -> "R":
             with self:
                 return await fn(*args, **kwargs)
 
+        inner._sentry_monitored = True  # type: ignore[attr-defined]
         return inner
 
     def _sync_wrapper(self, fn: "Callable[P, R]") -> "Callable[P, R]":
@@ -134,4 +135,5 @@ def inner(*args: "P.args", **kwargs: "P.kwargs") -> "R":
             with self:
                 return fn(*args, **kwargs)
 
+        inner._sentry_monitored = True  # type: ignore[attr-defined]
         return inner
diff --git a/sentry_sdk/crons/utils.py b/sentry_sdk/crons/utils.py
index d5fa55e500..01a70c1c1b 100644
--- a/sentry_sdk/crons/utils.py
+++ b/sentry_sdk/crons/utils.py
@@ -1,6 +1,9 @@
+import re
+from datetime import timedelta, timezone
 from typing import TYPE_CHECKING
 
 if TYPE_CHECKING:
+    from datetime import tzinfo
     from typing import Optional, Tuple
 
     from sentry_sdk._types import MonitorConfigSchedule, MonitorConfigScheduleUnit
@@ -27,3 +30,26 @@ def _get_interval_schedule(seconds: float) -> "Optional[MonitorConfigSchedule]":
                 "unit": unit,
             }
     return None
+
+
+# IANA zone names start with an uppercase letter. This rejects names like
+# "local" or "localtime" that tzlocal can give a zone.
+_IANA_TIMEZONE_NAME = re.compile(r"[A-Z][A-Za-z0-9._+-]*(?:/[A-Za-z0-9._+-]+)*")
+
+
+def _get_timezone_name(tz: "tzinfo") -> "Optional[str]":
+    """
+    Return the IANA name of the timezone, or None if it has none.
+    """
+    name = getattr(tz, "key", None) or getattr(tz, "zone", None)
+    if isinstance(name, str):
+        return name if _IANA_TIMEZONE_NAME.fullmatch(name) else None
+
+    if isinstance(tz, timezone):
+        offset = tz.utcoffset(None)
+        if offset % timedelta(hours=1):
+            return None
+        hours = offset // timedelta(hours=1)
+        return "Etc/GMT%+d" % -hours if hours else "UTC"
+
+    return None
diff --git a/sentry_sdk/integrations/arq.py b/sentry_sdk/integrations/arq.py
index 623dda3258..502fe0355d 100644
--- a/sentry_sdk/integrations/arq.py
+++ b/sentry_sdk/integrations/arq.py
@@ -1,10 +1,11 @@
 import sys
 import time
-from datetime import timedelta, timezone
+from functools import wraps
 
 import sentry_sdk
 from sentry_sdk.consts import OP, SPANDATA, SPANSTATUS
 from sentry_sdk.crons import monitor
+from sentry_sdk.crons.utils import _get_timezone_name
 from sentry_sdk.integrations import DidNotEnable, Integration, _check_minimum_version
 from sentry_sdk.integrations.logging import ignore_logger
 from sentry_sdk.scope import should_send_default_pii
@@ -221,6 +222,7 @@ def event_processor(event: "Event", hint: "Hint") -> "Optional[Event]":
 
 
 def _wrap_coroutine(name: str, coroutine: "WorkerCoroutine") -> "WorkerCoroutine":
+    @wraps(coroutine)
     async def _sentry_coroutine(
         ctx: "Dict[Any, Any]", *args: "Any", **kwargs: "Any"
     ) -> "Any":
@@ -326,6 +328,9 @@ def _monitor_cron_job(
         return
     cron_job._sentry_monitored = True
 
+    if getattr(cron_job.coroutine, "_sentry_monitored", False):
+        return
+
     # arq names cron jobs "cron:<function name>" by default.
     monitor_slug = cron_job.name
     if monitor_slug.startswith("cron:"):
@@ -393,7 +398,7 @@ def _get_crontab(cron_job: "CronJob") -> "Optional[str]":
     return " ".join(fields)  # type: ignore[arg-type]
 
 
-def _get_timezone_name(worker: "Worker") -> "Optional[str]":
+def _get_worker_timezone_name(worker: "Worker") -> "Optional[str]":
     tz = getattr(worker, "timezone", None)
     if tz is None:
         # Before arq 0.25, cron jobs ran in naive local time.
@@ -401,27 +406,15 @@ def _get_timezone_name(worker: "Worker") -> "Optional[str]":
             return "UTC"
         return None
 
-    # zoneinfo and pytz
-    name = getattr(tz, "key", None) or getattr(tz, "zone", None)
-    if isinstance(name, str):
-        return name
-
     # arq defaults to the system's fixed UTC offset at startup.
-    if isinstance(tz, timezone):
-        offset = tz.utcoffset(None)
-        if offset % timedelta(hours=1):
-            return None
-        hours = offset // timedelta(hours=1)
-        return "Etc/GMT%+d" % -hours if hours else "UTC"
-
-    return None
+    return _get_timezone_name(tz)
 
 
 def _get_monitor_config(
     cron_job: "CronJob", worker: "Worker"
 ) -> "Optional[MonitorConfig]":
     crontab = _get_crontab(cron_job)
-    timezone_name = _get_timezone_name(worker)
+    timezone_name = _get_worker_timezone_name(worker)
     if crontab is None or timezone_name is None:
         return None
     return {
diff --git a/tests/integrations/arq/test_arq_crons.py b/tests/integrations/arq/test_arq_crons.py
index 3087e6e594..88686e02b1 100644
--- a/tests/integrations/arq/test_arq_crons.py
+++ b/tests/integrations/arq/test_arq_crons.py
@@ -7,6 +7,7 @@
 from arq.connections import ArqRedis
 from fakeredis.aioredis import FakeRedis
 
+import sentry_sdk
 from sentry_sdk.integrations.arq import ArqIntegration, _get_monitor_config
 
 try:
@@ -183,6 +184,25 @@ async def test_cron_job_monitored_once(sentry_init, capture_envelopes):
     assert statuses[:4] == ["in_progress", "ok", "in_progress", "ok"]
 
 
+@sentry_sdk.monitor(monitor_slug="decorated")
+async def decorated_job(ctx):
+    pass
+
+
+@pytest.mark.asyncio
+async def test_monitor_decorated_cron_job_reports_once(sentry_init, capture_envelopes):
+    sentry_init(integrations=[ArqIntegration(monitor_cron_jobs=True)])
+    envelopes = capture_envelopes()
+
+    await _run_cron_jobs(
+        cron(decorated_job, run_at_startup=True), timezone=timezone.utc
+    )
+
+    check_ins = _check_ins(envelopes)
+    assert {c["monitor_slug"] for c in check_ins} == {"decorated"}
+    assert [c["status"] for c in check_ins[:2]] == ["in_progress", "ok"]
+
+
 class _Worker:
     def __init__(self, timezone):
         self.timezone = timezone