diff --git a/sky/dag.py b/sky/dag.py
index d6d9e09c5e1..47616a1a55d 100644
--- a/sky/dag.py
+++ b/sky/dag.py
@@ -74,8 +74,7 @@ def add(self, task: 'task.Task') -> None:
             ValueError: If the task already exists in the DAG or if its name
             is already used.
         """
-        if task.name is None:
-            task.name = common_utils.get_unique_task_name(task)
+        task.name = common_utils.get_unique_task_name(task)
         if task.name in self._task_name_lookup:
             with ux_utils.print_exception_no_traceback():
                 raise ValueError(
diff --git a/sky/serve/serve_utils.py b/sky/serve/serve_utils.py
index a9cf265b335..0ecf34135a7 100644
--- a/sky/serve/serve_utils.py
+++ b/sky/serve/serve_utils.py
@@ -37,7 +37,6 @@
 if typing.TYPE_CHECKING:
     import fastapi
 
-    from sky import task as task_lib
     from sky.serve import replica_managers
 
 SKY_SERVE_CONTROLLER_NAME: str = (
diff --git a/sky/utils/common_utils.py b/sky/utils/common_utils.py
index 72fcea27e49..b3f6aefea59 100644
--- a/sky/utils/common_utils.py
+++ b/sky/utils/common_utils.py
@@ -232,11 +232,10 @@ def get_global_job_id(job_timestamp: str,
     return global_job_id
 
 
-def get_unique_task_name(_: 'task_lib.Task') -> str:
-    timestamp = int(time.time())
+def get_unique_task_name(task: 'task_lib.Task') -> str:
+    name = task.name or f'task_{int(time.time())}'
     unique_suffix = uuid.uuid4().hex[:6]
-    name = f'task_{timestamp}_{unique_suffix}'
-    return name
+    return f'{name}_{unique_suffix}'
 
 
 class Backoff: