diff --git a/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/action/GetMigrationReindexStatusTransportAction.java b/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/action/GetMigrationReindexStatusTransportAction.java
index a823e1b2a12cf..db6dedb4bccc1 100644
--- a/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/action/GetMigrationReindexStatusTransportAction.java
+++ b/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/action/GetMigrationReindexStatusTransportAction.java
@@ -145,7 +145,7 @@ private void reportStatus(
     }
 
     /*
-     * This method feches doc counts for all indices in inProgressIndices (and the indices they are being reindexed into). After
+     * This method fetches doc counts for all indices in inProgressIndices (and the indices they are being reindexed into). After
      * successfully fetching those, reportStatus is called.
      */
     private void fetchInProgressStatsAndReportStatus(
diff --git a/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/task/ReindexDataStreamPersistentTaskExecutor.java b/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/task/ReindexDataStreamPersistentTaskExecutor.java
index 5a2f8a62bf924..6c69b7d6a19cb 100644
--- a/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/task/ReindexDataStreamPersistentTaskExecutor.java
+++ b/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/task/ReindexDataStreamPersistentTaskExecutor.java
@@ -94,7 +94,7 @@ protected ReindexDataStreamTask createTask(
             id,
             type,
             action,
-            "id=" + taskInProgress.getId(),
+            "Reindexing data stream " + taskInProgress.getParams().getSourceDataStream(),
             parentTaskId,
             headers
         );
diff --git a/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/task/ReindexDataStreamTask.java b/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/task/ReindexDataStreamTask.java
index 463f7f99d0a75..6f5bf280296e1 100644
--- a/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/task/ReindexDataStreamTask.java
+++ b/x-pack/plugin/migrate/src/main/java/org/elasticsearch/xpack/migrate/task/ReindexDataStreamTask.java
@@ -55,6 +55,7 @@ public ReindexDataStreamTask(
         this.persistentTaskStartTime = persistentTaskStartTime;
         this.initialTotalIndices = initialTotalIndices;
         this.initialTotalIndicesToBeUpgraded = initialTotalIndicesToBeUpgraded;
+        this.pending.set(initialTotalIndicesToBeUpgraded);
         this.completeTask = new RunOnce(() -> {
             if (exception == null) {
                 markAsCompleted();