BUG: (row) Index Name with to_html(header=False) is not displayed
State: closed

- [x] closes #23788
- [x] xref #24546
- [x] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry




Labels:
name: IO HTML
description: read_html, to_html, Styler.apply, Styler.applymap

Comments:
an you add a whatsnew note (ok to add to an existing one if we already have something similar)
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=h1) Report
> Merging [#24547](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/e76c90ed99efe6b2b827b10c01d759f85ece8045?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24547/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #24547      +/-   ##
==========================================
+ Coverage   92.32%   92.33%   +<.01%     
==========================================
  Files         166      166              
  Lines       52454    52462       +8     
==========================================
+ Hits        48430    48439       +9     
+ Misses       4024     4023       -1
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.75% <100%> (ø)` | :arrow_up: |
| #single | `43.01% <0%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/io/formats/html.py](https://codecov.io/gh/pandas-dev/pandas/pull/24547/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvaHRtbC5weQ==) | `99.03% <100%> (+0.35%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=footer). Last update [e76c90e...a24ca83](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=h1) Report
> Merging [#24547](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/e76c90ed99efe6b2b827b10c01d759f85ece8045?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24547/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #24547      +/-   ##
==========================================
+ Coverage   92.32%   92.33%   +<.01%     
==========================================
  Files         166      166              
  Lines       52454    52463       +9     
==========================================
+ Hits        48430    48440      +10     
+ Misses       4024     4023       -1
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.75% <100%> (ø)` | :arrow_up: |
| #single | `43% <0%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/io/formats/html.py](https://codecov.io/gh/pandas-dev/pandas/pull/24547/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvaHRtbC5weQ==) | `99.03% <100%> (+0.35%)` | :arrow_up: |
| [pandas/plotting/\_core.py](https://codecov.io/gh/pandas-dev/pandas/pull/24547/diff?src=pr&el=tree#diff-cGFuZGFzL3Bsb3R0aW5nL19jb3JlLnB5) | `83.76% <0%> (ø)` | :arrow_up: |
| [pandas/plotting/\_style.py](https://codecov.io/gh/pandas-dev/pandas/pull/24547/diff?src=pr&el=tree#diff-cGFuZGFzL3Bsb3R0aW5nL19zdHlsZS5weQ==) | `77.65% <0%> (+0.24%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=footer). Last update [e76c90e...c9ccd88](https://codecov.io/gh/pandas-dev/pandas/pull/24547?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

thanks @simonjayhawkins