diff --git a/pkg/util/mount/mount_helper.go b/pkg/util/mount/mount_helper.go
index fcbc37a639..a06871e478 100644
--- a/pkg/util/mount/mount_helper.go
+++ b/pkg/util/mount/mount_helper.go
@@ -24,18 +24,12 @@ import (
 	"k8s.io/klog"
 )
 
-// UnmountPath is a common unmount routine that unmounts the given path and
-// deletes the remaining directory if successful.
-func UnmountPath(mountPath string, mounter Interface) error {
-	return UnmountMountPoint(mountPath, mounter, false /* extensiveMountPointCheck */)
-}
-
-// UnmountMountPoint is a common unmount routine that unmounts the given path and
+// CleanupMountPoint unmounts the given path and
 // deletes the remaining directory if successful.
 // if extensiveMountPointCheck is true
 // IsNotMountPoint will be called instead of IsLikelyNotMountPoint.
-// IsNotMountPoint is more expensive but properly handles bind mounts.
-func UnmountMountPoint(mountPath string, mounter Interface, extensiveMountPointCheck bool) error {
+// IsNotMountPoint is more expensive but properly handles bind mounts within the same fs.
+func CleanupMountPoint(mountPath string, mounter Interface, extensiveMountPointCheck bool) error {
 	// mounter.ExistsPath cannot be used because for containerized kubelet, we need to check
 	// the path in the kubelet container, not on the host.
 	pathExists, pathErr := PathExists(mountPath)
@@ -47,16 +41,17 @@ func UnmountMountPoint(mountPath string, mounter Interface, extensiveMountPointC
 	if pathErr != nil && !corruptedMnt {
 		return fmt.Errorf("Error checking path: %v", pathErr)
 	}
-	return doUnmountMountPoint(mountPath, mounter, extensiveMountPointCheck, corruptedMnt)
+	return doCleanupMountPoint(mountPath, mounter, extensiveMountPointCheck, corruptedMnt)
 }
 
-// doUnmountMountPoint is a common unmount routine that unmounts the given path and
+// doCleanupMountPoint unmounts the given path and
 // deletes the remaining directory if successful.
 // if extensiveMountPointCheck is true
 // IsNotMountPoint will be called instead of IsLikelyNotMountPoint.
-// IsNotMountPoint is more expensive but properly handles bind mounts.
-// if corruptedMnt is true, it means that the mountPath is a corrupted mountpoint, Take it as an argument for convenience of testing
-func doUnmountMountPoint(mountPath string, mounter Interface, extensiveMountPointCheck bool, corruptedMnt bool) error {
+// IsNotMountPoint is more expensive but properly handles bind mounts within the same fs.
+// if corruptedMnt is true, it means that the mountPath is a corrupted mountpoint, and the mount point check
+// will be skipped
+func doCleanupMountPoint(mountPath string, mounter Interface, extensiveMountPointCheck bool, corruptedMnt bool) error {
 	if !corruptedMnt {
 		var notMnt bool
 		var err error
diff --git a/pkg/util/mount/mount_helper_test.go b/pkg/util/mount/mount_helper_test.go
index e8da449f9e..3afcca3798 100644
--- a/pkg/util/mount/mount_helper_test.go
+++ b/pkg/util/mount/mount_helper_test.go
@@ -25,7 +25,7 @@ import (
 	"testing"
 )
 
-func TestDoUnmountMountPoint(t *testing.T) {
+func TestDoCleanupMountPoint(t *testing.T) {
 	const testMount = "test-mount"
 	const defaultPerm = 0750
 
@@ -92,7 +92,7 @@ func TestDoUnmountMountPoint(t *testing.T) {
 				MountCheckErrors: map[string]error{mountPoint.Path: mountError},
 			}
 
-			err = doUnmountMountPoint(mountPoint.Path, fake, true, tt.corruptedMnt)
+			err = doCleanupMountPoint(mountPoint.Path, fake, true, tt.corruptedMnt)
 			if tt.expectErr {
 				if err == nil {
 					t.Errorf("test %s failed, expected error, got none", name)
diff --git a/pkg/util/mount/mount_linux.go b/pkg/util/mount/mount_linux.go
index 12a6590f15..85a9016968 100644
--- a/pkg/util/mount/mount_linux.go
+++ b/pkg/util/mount/mount_linux.go
@@ -934,11 +934,11 @@ func doCleanSubPath(mounter Interface, fullContainerDirPath, subPathIndex string
 	klog.V(4).Infof("Cleaning up subpath mounts for subpath %v", subPathIndex)
 	fullSubPath := filepath.Join(fullContainerDirPath, subPathIndex)
 
-	if err := UnmountMountPoint(fullSubPath, mounter, true); err != nil {
-		return fmt.Errorf("error unmounting %s: %s", fullSubPath, err)
+	if err := CleanupMountPoint(fullSubPath, mounter, true); err != nil {
+		return fmt.Errorf("error cleaning subpath mount %s: %s", fullSubPath, err)
 	}
 
-	klog.V(5).Infof("Removed %s", fullSubPath)
+	klog.V(4).Infof("Successfully cleaned subpath directory %s", fullSubPath)
 	return nil
 }
 
diff --git a/pkg/volume/util/util.go b/pkg/volume/util/util.go
index e3a6e8ed05..18e24d69f0 100644
--- a/pkg/volume/util/util.go
+++ b/pkg/volume/util/util.go
@@ -127,9 +127,9 @@ func SetReady(dir string) {
 
 // UnmountPath is a common unmount routine that unmounts the given path and
 // deletes the remaining directory if successful.
-// TODO: Change callers to call mount pkg directly
+// TODO: Remove this function and change callers to call mount pkg directly
 func UnmountPath(mountPath string, mounter mount.Interface) error {
-	return mount.UnmountMountPoint(mountPath, mounter, false /* extensiveMountPointCheck */)
+	return mount.CleanupMountPoint(mountPath, mounter, false /* extensiveMountPointCheck */)
 }
 
 // UnmountMountPoint is a common unmount routine that unmounts the given path and
@@ -139,7 +139,7 @@ func UnmountPath(mountPath string, mounter mount.Interface) error {
 // IsNotMountPoint is more expensive but properly handles bind mounts.
 // TODO: Change callers to call mount pkg directly
 func UnmountMountPoint(mountPath string, mounter mount.Interface, extensiveMountPointCheck bool) error {
-	return mount.UnmountMountPoint(mountPath, mounter, extensiveMountPointCheck)
+	return mount.CleanupMountPoint(mountPath, mounter, extensiveMountPointCheck)
 }
 
 // PathExists returns true if the specified path exists.