diff --git a/pkg/common/label.go b/pkg/common/label.go
index acf4b5cff3e..6c604b8d66f 100644
--- a/pkg/common/label.go
+++ b/pkg/common/label.go
@@ -29,8 +29,12 @@ const (
 	LabelAnnotationDataset = LabelAnnotationPrefix + "dataset"
 	// LabelAnnotationDatasetNum indicates the number of the dataset in specific node
 	LabelAnnotationDatasetNum = LabelAnnotationPrefix + "dataset-num"
-	// LabelAnnotationWrappedBy indicates the resource is wrapped by some dataset
-	LabelAnnotationWrappedBy = LabelAnnotationPrefix + "wrapped-by"
+
+	// LabelAnnotationManagedByDeprecated is a deprecated label key for LabelAnnotationManagedBy
+	LabelAnnotationManagedByDeprecated = LabelAnnotationPrefix + "wrapped-by"
+
+	// LabelAnnotationManagedBy indicates a pvc that is managed by Fluid
+	LabelAnnotationManagedBy = LabelAnnotationPrefix + "managed-by"
 
 	// fluid adminssion webhook inject flag
 	EnableFluidInjectionFlag = LabelAnnotationPrefix + "enable-injection"
@@ -124,3 +128,14 @@ func CheckExpectValue(m map[string]string, key string, targetValue string) bool
 	}
 	return false
 }
+
+func GetManagerDatasetFromLabels(labels map[string]string) (datasetName string, exists bool) {
+	datasetName, exists = labels[LabelAnnotationManagedBy]
+	if exists {
+		return
+	}
+
+	// fallback to check deprecated "fluid.io/wrapped-by" label
+	datasetName, exists = labels[LabelAnnotationManagedByDeprecated]
+	return
+}
diff --git a/pkg/ddc/thin/wrap_pvc.go b/pkg/ddc/thin/wrap_pvc.go
index 4c3b168c128..46ecad16d86 100644
--- a/pkg/ddc/thin/wrap_pvc.go
+++ b/pkg/ddc/thin/wrap_pvc.go
@@ -98,9 +98,9 @@ func (t *ThinEngine) wrapMountedPersistentVolumeClaim() (err error) {
 				return err
 			}
 
-			if _, exists := mountedPvc.Labels[common.LabelAnnotationWrappedBy]; !exists {
+			if _, exists := mountedPvc.Labels[common.LabelAnnotationManagedBy]; !exists {
 				labelsToModify := common.LabelsToModify{}
-				labelsToModify.Add(common.LabelAnnotationWrappedBy, t.name)
+				labelsToModify.Add(common.LabelAnnotationManagedBy, t.name)
 				_, err = utils.PatchLabels(t.Client, mountedPvc, labelsToModify)
 				if err != nil {
 					return err
@@ -130,9 +130,9 @@ func (t *ThinEngine) unwrapMountedPersistentVolumeClaims() (err error) {
 				return errors.Wrapf(err, "failed to get pvc when unwrapping pvc %s", pvcName)
 			}
 
-			if wrappedBy, exists := pvc.Labels[common.LabelAnnotationWrappedBy]; exists && wrappedBy == t.name {
+			if wrappedBy, exists := pvc.Labels[common.LabelAnnotationManagedBy]; exists && wrappedBy == t.name {
 				labelsToModify := common.LabelsToModify{}
-				labelsToModify.Delete(common.LabelAnnotationWrappedBy)
+				labelsToModify.Delete(common.LabelAnnotationManagedBy)
 				if _, err = utils.PatchLabels(t.Client, pvc, labelsToModify); err != nil {
 					return errors.Wrapf(err, "failed to remove label when unwrapping pvc %s", pvc.Name)
 				}
diff --git a/pkg/ddc/thin/wrap_pvc_test.go b/pkg/ddc/thin/wrap_pvc_test.go
index 37bf8079ffa..b513c88be2f 100644
--- a/pkg/ddc/thin/wrap_pvc_test.go
+++ b/pkg/ddc/thin/wrap_pvc_test.go
@@ -60,7 +60,7 @@ func TestThinEngine_wrapMountedPersistentVolumeClaim(t *testing.T) {
 				Name:      "my-pvc-2",
 				Namespace: "default",
 				Labels: map[string]string{
-					common.LabelAnnotationWrappedBy: "dataset2",
+					common.LabelAnnotationManagedBy: "dataset2",
 				},
 			},
 		},
@@ -119,10 +119,10 @@ func TestThinEngine_wrapMountedPersistentVolumeClaim(t *testing.T) {
 				t.Errorf("Got error when checking pvc labels: %v", err)
 			}
 
-			if wrappedBy, exists := pvc.Labels[common.LabelAnnotationWrappedBy]; !exists {
-				t.Errorf("Expect get label \"%s=%s\" on pvc, but not exists", common.LabelAnnotationWrappedBy, engine.name)
+			if wrappedBy, exists := pvc.Labels[common.LabelAnnotationManagedBy]; !exists {
+				t.Errorf("Expect get label \"%s=%s\" on pvc, but not exists", common.LabelAnnotationManagedBy, engine.name)
 			} else if wrappedBy != engine.name {
-				t.Errorf("Expect get label \"%s=%s\" on pvc, but got %s", common.LabelAnnotationWrappedBy, engine.name, wrappedBy)
+				t.Errorf("Expect get label \"%s=%s\" on pvc, but got %s", common.LabelAnnotationManagedBy, engine.name, wrappedBy)
 			}
 		})
 	}
@@ -137,7 +137,7 @@ func TestThinEngine_unwrapMountedPersistentVolumeClaims(t *testing.T) {
 				Name:      "my-pvc-1",
 				Namespace: "default",
 				Labels: map[string]string{
-					common.LabelAnnotationWrappedBy: "dataset1",
+					common.LabelAnnotationManagedBy: "dataset1",
 				},
 			},
 		},
@@ -236,8 +236,8 @@ func TestThinEngine_unwrapMountedPersistentVolumeClaims(t *testing.T) {
 				t.Errorf("Got error when checking pvc labels: %v", err)
 			}
 
-			if _, exists := pvc.Labels[common.LabelAnnotationWrappedBy]; exists {
-				t.Errorf("Expect no label \"%s\" on pvc, but it exists. pvc Labels: %v", common.LabelAnnotationWrappedBy, pvc.Labels)
+			if _, exists := pvc.Labels[common.LabelAnnotationManagedBy]; exists {
+				t.Errorf("Expect no label \"%s\" on pvc, but it exists. pvc Labels: %v", common.LabelAnnotationManagedBy, pvc.Labels)
 			}
 		})
 	}
diff --git a/pkg/utils/kubeclient/volume.go b/pkg/utils/kubeclient/volume.go
index 1ab3f6f405c..1d0bfd3b802 100644
--- a/pkg/utils/kubeclient/volume.go
+++ b/pkg/utils/kubeclient/volume.go
@@ -364,7 +364,7 @@ func CheckIfPVCIsDataset(pvc *v1.PersistentVolumeClaim) (isDataset bool) {
 	}
 	_, isDataset = pvc.Labels[common.LabelAnnotationStorageCapacityPrefix+namespace+"-"+name]
 
-	if _, exists := pvc.Labels[common.LabelAnnotationWrappedBy]; exists {
+	if _, exists := common.GetManagerDatasetFromLabels(pvc.Labels); exists {
 		isDataset = true
 	}
 
diff --git a/pkg/webhook/scheduler/mutating/utils.go b/pkg/webhook/scheduler/mutating/utils.go
index a665f8342fd..6cf65b0fd4f 100644
--- a/pkg/webhook/scheduler/mutating/utils.go
+++ b/pkg/webhook/scheduler/mutating/utils.go
@@ -25,8 +25,8 @@ func buildRuntimeInfoInternal(client client.Client,
 		namespace = corev1.NamespaceDefault
 	}
 	pvcName := pvc.GetName()
-	if wrapperName, exists := pvc.Labels[common.LabelAnnotationWrappedBy]; exists {
-		pvcName = wrapperName
+	if datasetName, exists := common.GetManagerDatasetFromLabels(pvc.Labels); exists {
+		pvcName = datasetName
 	}
 
 	dataset, err := utils.GetDataset(client, pvcName, namespace)