BUG: read_parquet doesn't handle index names correctly

[zmbc]

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Reproducible Example

import pandas

my_data = pandas.DataFrame({'a': range(10), 'b': range(10, 20)})
my_data.index.name = "foobar"

my_data.to_parquet("index_with_name.parquet")

import modin.pandas

modin.pandas.read_parquet("index_with_name.parquet")

Issue Description

read_parquet errors instead of loading the dataframe.

Note that this was the case before #6442 -- it is not related to filters or to the code change to accommodate them.

Expected Behavior

Pandas behavior:

# Check that the engine doesn't matter
df_pyarrow = pandas.read_parquet("index_with_name.parquet", engine="pyarrow")
df_fastparquet = pandas.read_parquet("index_with_name.parquet", engine="fastparquet")

assert df_pyarrow.equals(df_fastparquet)

print(df_pyarrow)

gives

        a   b
foobar       
0       0  10
1       1  11
2       2  12
3       3  13
4       4  14
5       5  15
6       6  16
7       7  17
8       8  18
9       9  19

Error Logs

Traceback (most recent call last):
  File "~/src/modin/test_index_with_name.py", line 20, in <module>
    modin.pandas.read_parquet("index_with_name.parquet")
  File "~/src/modin/modin/utils.py", line 475, in wrapped
    return func(*params.args, **params.kwargs)
  File "~/src/modin/modin/logging/logger_decorator.py", line 128, in run_and_log
    return obj(*args, **kwargs)
  File "~/src/modin/modin/pandas/io.py", line 297, in read_parquet
    query_compiler=FactoryDispatcher.read_parquet(
  File "~/src/modin/modin/core/execution/dispatching/factories/dispatcher.py", line 195, in read_parquet
    return cls.get_factory()._read_parquet(**kwargs)
  File "~/src/modin/modin/core/execution/dispatching/factories/factories.py", line 213, in _read_parquet
    return cls.io_cls.read_parquet(**kwargs)
  File "~/src/modin/modin/logging/logger_decorator.py", line 128, in run_and_log
    return obj(*args, **kwargs)
  File "~/src/modin/modin/core/io/file_dispatcher.py", line 159, in read
    query_compiler = cls._read(*args, **kwargs)
  File "~/src/modin/modin/logging/logger_decorator.py", line 128, in run_and_log
    return obj(*args, **kwargs)
  File "~/src/modin/modin/core/io/column_stores/parquet_dispatcher.py", line 725, in _read
    return cls.build_query_compiler(
  File "~/src/modin/modin/logging/logger_decorator.py", line 128, in run_and_log
    return obj(*args, **kwargs)
  File "~/src/modin/modin/core/io/column_stores/parquet_dispatcher.py", line 601, in build_query_compiler
    index, sync_index = cls.build_index(
  File "~/src/modin/modin/logging/logger_decorator.py", line 128, in run_and_log
    return obj(*args, **kwargs)
  File "~/src/modin/modin/core/io/column_stores/parquet_dispatcher.py", line 551, in build_index
    complete_index = dataset.to_pandas_dataframe(
  File "~/src/modin/modin/core/io/column_stores/parquet_dispatcher.py", line 236, in to_pandas_dataframe
    return read_table(
  File "~/mambaforge/envs/modin/lib/python3.10/site-packages/pyarrow/parquet/core.py", line 2986, in read_table
    return dataset.read(columns=columns, use_threads=use_threads,
  File "~/mambaforge/envs/modin/lib/python3.10/site-packages/pyarrow/parquet/core.py", line 2614, in read
    table = self._dataset.to_table(
  File "pyarrow/_dataset.pyx", line 537, in pyarrow._dataset.Dataset.to_table
  File "pyarrow/_dataset.pyx", line 383, in pyarrow._dataset.Dataset.scanner
  File "pyarrow/_dataset.pyx", line 3202, in pyarrow._dataset.Scanner.from_dataset
  File "pyarrow/_dataset.pyx", line 3120, in pyarrow._dataset.Scanner._make_scan_options
  File "pyarrow/_dataset.pyx", line 3071, in pyarrow._dataset._populate_builder
  File "pyarrow/error.pxi", line 100, in pyarrow.lib.check_status
pyarrow.lib.ArrowInvalid: No match for FieldRef.Name(foobar) in a: int64
b: int64
__fragment_index: int32
__batch_index: int32
__last_in_fragment: bool
__filename: string

Installed Versions

INSTALLED VERSIONS

commit : ba1cccd19da778f0c3a7d6a885685da16a072870
python : 3.10.12.final.0
python-bits : 64
OS : Linux
OS-release : 5.4.0-135-generic
Version : #152-Ubuntu SMP Wed Nov 23 20:19:22 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.1.0
numpy : 1.25.1
pytz : 2023.3
dateutil : 2.8.2
setuptools : 68.0.0
pip : 23.2.1
Cython : None
pytest : 7.4.0
hypothesis : None
sphinx : 7.1.0
blosc : None
feather : 0.4.1
xlsxwriter : None
lxml.etree : 4.9.3
html5lib : None
pymysql : None
psycopg2 : 2.9.6
jinja2 : 3.1.2
IPython : 8.14.0
pandas_datareader : None
bs4 : 4.12.2
bottleneck : None
dataframe-api-compat: None
fastparquet : 2022.12.0
fsspec : 2023.6.0
gcsfs : None
matplotlib : 3.7.2
numba : None
numexpr : 2.8.4
odfpy : None
openpyxl : 3.1.2
pandas_gbq : 0.15.0
pyarrow : 12.0.1
pyreadstat : None
pyxlsb : None
s3fs : 2023.6.0
scipy : 1.11.1
sqlalchemy : 1.4.45
tables : 3.8.0
tabulate : None
xarray : None
xlrd : 2.0.1
zstandard : None
tzdata : 2023.3
qtpy : 2.3.1
pyqt5 : None