Repository: pandas-dev/pandas (python)

Issue:
BUG: 
### Pandas version checks

- [X] I have checked that this issue has not already been reported.

- [X] I have confirmed this bug exists on the [latest version](https://pandas.pydata.org/docs/whatsnew/index.html) of pandas.

- [X] I have confirmed this bug exists on the [main branch](https://pandas.pydata.org/docs/dev/getting_started/install.html#installing-the-development-version-of-pandas) of pandas.


### Reproducible Example

```python
import io
import pandas as pd

df = pd.DataFrame(data={'index':[1,2], 'a': [2,3]})
s = df.to_json(orient="table")
df = pd.read_json(io.StringIO(s), orient="table")
```



### Issue Description

`read_json` failed with
```
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/io/json/_json.py", line 815, in read_json
    return json_reader.read()
           ^^^^^^^^^^^^^^^^^^
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/io/json/_json.py", line 1025, in read
    obj = self._get_object_parser(self.data)
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/io/json/_json.py", line 1051, in _get_object_parser
    obj = FrameParser(json, **kwargs).parse()
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/io/json/_json.py", line 1187, in parse
    self._parse()
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/io/json/_json.py", line 1427, in _parse
    self.obj = parse_table_schema(json, precise_float=self.precise_float)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/io/json/_table_schema.py", line 380, in parse_table_schema
    df = df.set_index(table["schema"]["primaryKey"])
         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/core/frame.py", line 6178, in set_index
    index = ensure_index_from_sequences(arrays, names)
            ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/core/indexes/base.py", line 7588, in ensure_index_from_sequences
    return Index(sequences[0], name=names)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/core/indexes/base.py", line 528, in __new__
    return cls(np.asarray(data), dtype=dtype, copy=copy, name=name)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/ranbi/vsa_cs/.venv/lib/python3.12/site-packages/pandas/core/indexes/base.py", line 570, in __new__
    raise ValueError("Index data must be 1-dimensional") from err
ValueError: Index data must be 1-dimensional
```

### Expected Behavior

`read_json` should return the same df as the original one

```
   index  a
0      1  2
1      2  3
```

### Installed Versions

<details>



INSTALLED VERSIONS
------------------
commit                : d9cdd2ee5a58015ef6f4d15c7226110c9aab8140
python                : 3.12.2.final.0
python-bits           : 64
OS                    : Darwin
OS-release            : 23.1.0
Version               : Darwin Kernel Version 23.1.0: Mon Oct  9 21:33:00 PDT 2023; root:xnu-10002.41.9~7/RELEASE_ARM64_T6031
machine               : arm64
processor             : arm
byteorder             : little
LC_ALL                : None
LANG                  : en_US.UTF-8
LOCALE                : en_US.UTF-8

pandas                : 2.2.2
numpy                 : 1.26.3
pytz                  : 2024.1
dateutil              : 2.9.0.post0
setuptools            : 69.5.1
pip                   : 24.0
Cython                : None
pytest                : 8.0.0
hypothesis            : None
sphinx                : None
blosc                 : None
feather               : None
xlsxwriter            : 3.2.0
lxml.etree            : 5.2.2
html5lib              : None
pymysql               : None
psycopg2              : None
jinja2                : 3.1.3
IPython               : 8.12.3
pandas_datareader     : None
adbc-driver-postgresql: None
adbc-driver-sqlite    : None
bs4                   : 4.12.3
bottleneck            : None
dataframe-api-compat  : None
fastparquet           : None
fsspec                : 2024.3.1
gcsfs                 : None
matplotlib            : 3.8.2
numba                 : None
numexpr               : None
odfpy                 : None
openpyxl              : 3.1.2
pandas_gbq            : None
pyarrow               : 15.0.2
pyreadstat            : None
python-calamine       : None
pyxlsb                : None
s3fs                  : None
scipy                 : 1.13.0
sqlalchemy            : None
tables                : None
tabulate              : 0.9.0
xarray                : None
xlrd                  : None
zstandard             : 0.22.0
tzdata                : 2024.1
qtpy                  : None
pyqt5                 : None

</details>


Pull request description:
BUG: make JSONTableWriter fail if no index.name and 'index' in columns
This commit is intended to fix GH #58925. If index.name is empty it will use set_default_names inside __init__ to make check on overlapping names fail. Otherwise it's done during schema creation and not reflected on the dataframe itself which creates inconsistency between the data and its schema.

Probably new behavior should be mentioned in the `to_json` docs? I added the docs change as a separate commit to ease squashing or reverting. 

- [x] closes #58925
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.


Patch:
diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index 0acb82ffec..2025474fec 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -559,6 +559,7 @@ MultiIndex
 I/O
 ^^^
 - Bug in :class:`DataFrame` and :class:`Series` ``repr`` of :py:class:`collections.abc.Mapping`` elements. (:issue:`57915`)
+- Bug in :meth:`.DataFrame.to_json` when ``"index"`` was a value in the :attr:`DataFrame.column` and :attr:`Index.name` was ``None``. Now, this will fail with a ``ValueError`` (:issue:`58925`)
 - Bug in :meth:`DataFrame.to_dict` raises unnecessary ``UserWarning`` when columns are not unique and ``orient='tight'``. (:issue:`58281`)
 - Bug in :meth:`DataFrame.to_excel` when writing empty :class:`DataFrame` with :class:`MultiIndex` on both axes (:issue:`57696`)
 - Bug in :meth:`DataFrame.to_stata` when writing :class:`DataFrame` and ``byteorder=`big```. (:issue:`58969`)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 5d9e04bd50..2a0495dff6 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -2387,7 +2387,8 @@ class NDFrame(PandasObject, indexing.IndexingMixin):
         index : bool or None, default None
             The index is only used when 'orient' is 'split', 'index', 'column',
             or 'table'. Of these, 'index' and 'column' do not support
-            `index=False`.
+            `index=False`. The string 'index' as a column name with empty :class:`Index`
+            or if it is 'index' will raise a ``ValueError``.
 
         indent : int, optional
            Length of whitespace used to indent each record.
diff --git a/pandas/io/json/_json.py b/pandas/io/json/_json.py
index 24fcb78a41..b29ead1d14 100644
--- a/pandas/io/json/_json.py
+++ b/pandas/io/json/_json.py
@@ -59,6 +59,7 @@ from pandas.io.json._normalize import convert_to_line_delimits
 from pandas.io.json._table_schema import (
     build_table_schema,
     parse_table_schema,
+    set_default_names,
 )
 from pandas.io.parsers.readers import validate_integer
 
@@ -353,6 +354,8 @@ class JSONTableWriter(FrameWriter):
             raise ValueError(msg)
 
         self.schema = build_table_schema(obj, index=self.index)
+        if self.index:
+            obj = set_default_names(obj)
 
         # NotImplemented on a column MultiIndex
         if obj.ndim == 2 and isinstance(obj.columns, MultiIndex):


Test patch:
diff --git a/pandas/tests/io/json/test_pandas.py b/pandas/tests/io/json/test_pandas.py
index e00c193fd4..a34c0adc69 100644
--- a/pandas/tests/io/json/test_pandas.py
+++ b/pandas/tests/io/json/test_pandas.py
@@ -1610,6 +1610,13 @@ class TestPandasContainer:
         )
         tm.assert_frame_equal(result, expected)
 
+    def test_to_json_with_index_as_a_column_name(self):
+        df = DataFrame(data={"index": [1, 2], "a": [2, 3]})
+        with pytest.raises(
+            ValueError, match="Overlapping names between the index and columns"
+        ):
+            df.to_json(orient="table")
+
     @pytest.mark.parametrize("dtype", [True, {"b": int, "c": int}])
     def test_read_json_table_dtype_raises(self, dtype):
         # GH21345