diff --git a/tests/test_toml_document.py b/tests/test_toml_document.py
index 1cdfb9c..7e6bfa1 100644
--- a/tests/test_toml_document.py
+++ b/tests/test_toml_document.py
@@ -965,6 +965,20 @@ def test_replace_preserve_sep() -> None:
     )
 
 
+def test_replace_table_with_itself_preserves_display_name() -> None:
+    content = """\
+[keys.a]
+[keys .'a'.'c']
+  'd'\t= 'e'
+"""
+    doc = parse(content)
+
+    for mode in doc["keys"]:
+        doc["keys"][mode] = doc["keys"][mode]
+
+    assert doc.as_string() == content
+
+
 def test_replace_with_table_of_nested() -> None:
     example = """\
     [a]
diff --git a/tomlkit/container.py b/tomlkit/container.py
index 75e0901..5c579a6 100644
--- a/tomlkit/container.py
+++ b/tomlkit/container.py
@@ -862,7 +862,7 @@ def _replace_at(
                 value.trivia.trail = v.trivia.trail
             self._body[idx] = (new_key, value)
 
-        if hasattr(value, "invalidate_display_name"):
+        if value is not v and hasattr(value, "invalidate_display_name"):
             value.invalidate_display_name()
 
         if isinstance(value, Table):