diff --git a/dask_kubernetes/operator/controller/controller.py b/dask_kubernetes/operator/controller/controller.py
index 62cf63dfd..1a01ed905 100644
--- a/dask_kubernetes/operator/controller/controller.py
+++ b/dask_kubernetes/operator/controller/controller.py
@@ -72,7 +72,7 @@ def build_scheduler_deployment_spec(
         **{
             "dask.org/cluster-name": cluster_name,
             "dask.org/component": "scheduler",
-            "dask.org/object-name": name,
+            "dask.org/component-name": name,
             "sidecar.istio.io/inject": "false",
         }
     )
@@ -104,7 +104,7 @@ def build_scheduler_service_spec(cluster_name, spec, annotations, labels):
         **{
             "dask.org/cluster-name": cluster_name,
             "dask.org/component": "scheduler",
-            "dask.org/object-name": name,
+            "dask.org/component-name": name,
         }
     )
     return {
@@ -128,7 +128,7 @@ def build_worker_deployment_spec(
             "dask.org/cluster-name": cluster_name,
             "dask.org/workergroup-name": worker_group_name,
             "dask.org/component": "worker",
-            "dask.org/object-name": worker_name,
+            "dask.org/component-name": worker_name,
             "sidecar.istio.io/inject": "false",
         }
     )
@@ -183,7 +183,7 @@ def build_job_pod_spec(job_name, cluster_name, namespace, spec, annotations, lab
         **{
             "dask.org/cluster-name": cluster_name,
             "dask.org/component": "job-runner",
-            "dask.org/object-name": name,
+            "dask.org/component-name": name,
             "sidecar.istio.io/inject": "false",
         }
     )
@@ -217,7 +217,7 @@ def build_default_worker_group_spec(cluster_name, spec, annotations, labels):
         **{
             "dask.org/cluster-name": cluster_name,
             "dask.org/component": "workergroup",
-            "dask.org/object-name": name,
+            "dask.org/component-name": name,
         }
     )
     return {
@@ -239,7 +239,7 @@ def build_cluster_spec(name, worker_spec, scheduler_spec, annotations, labels):
     labels.update(
         **{
             "dask.org/cluster-name": name,
-            "dask.org/object-name": name,
+            "dask.org/component-name": name,
         }
     )
     return {
@@ -624,9 +624,6 @@ async def daskworkergroup_replica_update(
                 if (
                     worker_pod.status.phase
                     not in [
-                        "ContainerCreating",
-                        "Initializing",
-                        "Terminating",
                         "Running",
                     ]
                     and not await worker.ready()