diff --git a/task/backend/bolt/bolt.go b/task/backend/bolt/bolt.go
index c407d42967..14dcbe569c 100644
--- a/task/backend/bolt/bolt.go
+++ b/task/backend/bolt/bolt.go
@@ -3,13 +3,13 @@
 // The data stored in bolt is structured as follows:
 //
 //    bucket(/tasks/v1/tasks) key(:task_id) -> Content of submitted task (i.e. flux code).
-//    bucket(/tasks/v1/task_meta) Key(:task_id) -> Protocol Buffer encoded backend.StoreTaskMeta,
+//    bucket(/tasks/v1/task_meta) key(:task_id) -> Protocol Buffer encoded backend.StoreTaskMeta,
 //                                    so we have a consistent view of runs in progress and max concurrency.
 //    bucket(/tasks/v1/org_by_task_id) key(task_id) -> The organization ID (stored as encoded string) associated with given task.
 //    bucket(/tasks/v1/user_by_task_id) key(:task_id) -> The user ID (stored as encoded string) associated with given task.
 //    buket(/tasks/v1/name_by_task_id) key(:task_id) -> The user-supplied name of the script.
-//    bucket(/tasks/v1/name_by_org) key(:org_id) -> Task ID. This allows us to make task names unique for org
-//    bucket(/tasks/v1/name_by_user) key(:user_id)  -> Task ID. This allows us to make task names unique for user
+//    bucket(/tasks/v1/name_by_org).bucket(:org_id) key(:task_name) -> Task ID. This allows us to make task names unique for org.
+//    bucket(/tasks/v1/name_by_user).bucket(:user_id) key(:task_name)  -> Task ID. This allows us to make task names unique for user.
 //    bucket(/tasks/v1/run_ids) -> Counter for run IDs
 //    bucket(/tasks/v1/orgs).bucket(:org_id) key(:task_id) -> Empty content; presence of :task_id allows for lookup from org to tasks.
 //    bucket(/tasks/v1/users).bucket(:user_id) key(:task_id) -> Empty content; presence of :task_id allows for lookup from user to tasks.
@@ -522,7 +522,7 @@ func (s *Store) DisableTask(ctx context.Context, id platform.ID) error {
 	})
 }
 
-// DeleteTask deletes the task
+// DeleteTask deletes the task.
 func (s *Store) DeleteTask(ctx context.Context, id platform.ID) (deleted bool, err error) {
 	paddedID := padID(id)
 	err = s.db.Batch(func(tx *bolt.Tx) error {
@@ -530,6 +530,8 @@ func (s *Store) DeleteTask(ctx context.Context, id platform.ID) (deleted bool, e
 		if check := b.Bucket(tasksPath).Get(paddedID); check == nil {
 			return ErrNotFound
 		}
+		name := b.Bucket(nameByTaskID).Get(paddedID)
+
 		if err := b.Bucket(taskMetaPath).Delete(paddedID); err != nil {
 			return err
 		}
@@ -541,6 +543,9 @@ func (s *Store) DeleteTask(ctx context.Context, id platform.ID) (deleted bool, e
 			if err := b.Bucket(usersPath).Bucket(user).Delete(paddedID); err != nil {
 				return err
 			}
+			if err := b.Bucket(nameByUser).Bucket(user).Delete(name); err != nil {
+				return err
+			}
 		}
 		if err := b.Bucket(userByTaskID).Delete(paddedID); err != nil {
 			return err
@@ -554,6 +559,9 @@ func (s *Store) DeleteTask(ctx context.Context, id platform.ID) (deleted bool, e
 			if err := b.Bucket(orgsPath).Bucket(org).Delete(paddedID); err != nil {
 				return err
 			}
+			if err := b.Bucket(nameByOrg).Bucket(org).Delete(name); err != nil {
+				return err
+			}
 		}
 		return b.Bucket(orgByTaskID).Delete(paddedID)
 	})
diff --git a/task/backend/storetest/storetest.go b/task/backend/storetest/storetest.go
index e3e4955c98..6ba56144af 100644
--- a/task/backend/storetest/storetest.go
+++ b/task/backend/storetest/storetest.go
@@ -11,9 +11,12 @@ import (
 	"time"
 
 	"github.com/influxdata/platform"
+	"github.com/influxdata/platform/snowflake"
 	"github.com/influxdata/platform/task/backend"
 )
 
+var idGen = snowflake.NewIDGenerator()
+
 type CreateStoreFunc func(*testing.T) backend.Store
 type DestroyStoreFunc func(*testing.T, backend.Store)
 type TestFunc func(*testing.T, CreateStoreFunc, DestroyStoreFunc)
@@ -626,7 +629,8 @@ from(bucket:"test") |> range(start:-1h)`
 		s := create(t)
 		defer destroy(t, s)
 
-		id, err := s.CreateTask(context.Background(), []byte{1}, []byte{2}, script, 0)
+		org, user := idGen.ID(), idGen.ID()
+		id, err := s.CreateTask(context.Background(), org, user, script, 0)
 		if err != nil {
 			t.Fatal(err)
 		}
@@ -656,6 +660,20 @@ from(bucket:"test") |> range(start:-1h)`
 		if task != nil {
 			t.Fatalf("expected nil task when finding nonexistent ID, got %#v", task)
 		}
+
+		// It's safe to reuse the same name, for the same org with a new user, after deleting the original.
+		id, err = s.CreateTask(context.Background(), org, idGen.ID(), script, 0)
+		if err != nil {
+			t.Fatalf("Error when reusing task name that was previously deleted: %v", err)
+		}
+		if _, err := s.DeleteTask(context.Background(), id); err != nil {
+			t.Fatal(err)
+		}
+
+		// Reuse the same name, for the original user but a new org.
+		if _, err = s.CreateTask(context.Background(), idGen.ID(), user, script, 0); err != nil {
+			t.Fatalf("Error when reusing task name that was previously deleted: %v", err)
+		}
 	})
 }