DEPR Rename keyword "quantile" to "q" in `Rolling.quantile`
- [x] Closes #52550
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests)
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit)
- [x] Added an entry in the latest `doc/source/whatsnew/v2.1.0.rst` file

Could you deprecate this on `Expanding` too? In rolling.py there's also this "private" quantile function

```
    def quantile(
        self,
        quantile: float,
        interpolation: QuantileInterpolation = "linear",
        numeric_only: bool = False,
    ):
```

could you change `quantile` to `q` here too? > In rolling.py there's also this "private" quantile function, could you change `quantile` to `q` here too?

Sure, and since it is a private function, no deprecation is needed right? > Sure, and since it is a private function, no deprecation is needed right?

Correct Thanks @Charlie-XIAO 