diff --git a/changelog.d/6565.misc b/changelog.d/6565.misc
new file mode 100644
index 000000000..e83f245bf
--- /dev/null
+++ b/changelog.d/6565.misc
@@ -0,0 +1 @@
+Add assertion that schema delta file names are unique.
diff --git a/synapse/storage/prepare_database.py b/synapse/storage/prepare_database.py
index 0195edf4a..403848ad0 100644
--- a/synapse/storage/prepare_database.py
+++ b/synapse/storage/prepare_database.py
@@ -18,6 +18,7 @@ import imp
 import logging
 import os
 import re
+from collections import Counter
 
 import attr
 
@@ -315,6 +316,9 @@ def _upgrade_existing_database(
                 )
             )
 
+        # Used to check if we have any duplicate file names
+        file_name_counter = Counter()
+
         # Now find which directories have anything of interest.
         directory_entries = []
         for directory in directories:
@@ -325,6 +329,9 @@ def _upgrade_existing_database(
                     _DirectoryListing(file_name, os.path.join(directory, file_name))
                     for file_name in file_names
                 )
+
+                for file_name in file_names:
+                    file_name_counter[file_name] += 1
             except FileNotFoundError:
                 # Data stores can have empty entries for a given version delta.
                 pass
@@ -333,6 +340,17 @@ def _upgrade_existing_database(
                     "Could not open delta dir for version %d: %s" % (v, directory)
                 )
 
+        duplicates = set(
+            file_name for file_name, count in file_name_counter.items() if count > 1
+        )
+        if duplicates:
+            # We don't support using the same file name in the same delta version.
+            raise PrepareDatabaseException(
+                "Found multiple delta files with the same name in v%d: %s",
+                v,
+                duplicates,
+            )
+
         # We sort to ensure that we apply the delta files in a consistent
         # order (to avoid bugs caused by inconsistent directory listing order)
         directory_entries.sort()