diff --git a/pymongo/server.py b/pymongo/server.py
index 985d45acb..f431fd014 100644
--- a/pymongo/server.py
+++ b/pymongo/server.py
@@ -132,6 +132,8 @@ class Server:
 
         if publish:
             cmd, dbn = operation.as_command(conn)
+            if "$db" not in cmd:
+                cmd["$db"] = dbn
             assert listeners is not None
             listeners.publish_command_start(
                 cmd, dbn, request_id, conn.address, service_id=conn.service_id
diff --git a/test/test_cursor.py b/test/test_cursor.py
index f8820f8aa..37c0335fa 100644
--- a/test/test_cursor.py
+++ b/test/test_cursor.py
@@ -22,6 +22,8 @@ import sys
 import threading
 import time
 
+import pymongo
+
 sys.path[0:0] = [""]
 
 from test import IntegrationTest, client_context, unittest
@@ -1586,6 +1588,28 @@ class TestRawBatchCommandCursor(IntegrationTest):
             n += 4
             listener.reset()
 
+    @client_context.require_version_min(5, 0, -1)
+    @client_context.require_no_mongos
+    def test_exhaust_cursor_db_set(self):
+        listener = OvertCommandListener()
+        client = rs_or_single_client(event_listeners=[listener])
+        self.addCleanup(client.close)
+        c = client.pymongo_test.test
+        c.delete_many({})
+        c.insert_many([{"_id": i} for i in range(3)])
+
+        listener.reset()
+
+        result = list(c.find({}, cursor_type=pymongo.CursorType.EXHAUST, batch_size=1))
+
+        self.assertEqual(len(result), 3)
+
+        self.assertEqual(
+            listener.started_command_names(), ["find", "getMore", "getMore", "getMore"]
+        )
+        for cmd in listener.started_events:
+            self.assertEqual(cmd.command["$db"], "pymongo_test")
+
 
 if __name__ == "__main__":
     unittest.main()