diff --git a/tests/examples/table_names_with_string_delimiters.toml b/tests/examples/table_names_with_string_delimiters.toml
new file mode 100644
index 00000000..8efd3efb
--- /dev/null
+++ b/tests/examples/table_names_with_string_delimiters.toml
@@ -0,0 +1,5 @@
+['Special "table"']
+foo = "bar"
+
+["BJ's Restaurant"]
+account = "dining"
diff --git a/tests/test_api.py b/tests/test_api.py
index 86b589b8..a19bddaf 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -53,6 +53,7 @@ def json_serial(obj):
         "newline_in_strings",
         "preserve_quotes_in_string",
         "string_slash_whitespace_newline",
+        "table_names_with_string_delimiters",
     ],
 )
 def test_parse_can_parse_valid_toml_files(example, example_name):
diff --git a/tomlkit/parser.py b/tomlkit/parser.py
index ecb2a752..0ff26f09 100644
--- a/tomlkit/parser.py
+++ b/tomlkit/parser.py
@@ -219,7 +219,12 @@ def _split_table_name(self, name):  # type: (str) -> Generator[Key]
                 continue
             elif c in {"'", '"'}:
                 if in_name:
-                    if t == KeyType.Literal and c == '"':
+                    if (
+                        t == KeyType.Literal
+                        and c == '"'
+                        or t == KeyType.Basic
+                        and c == "'"
+                    ):
                         current += c
                         continue