Summary

The **kwargs are not typically listed in the function, but instead the final destination of the **kwargs is mentioned. For example:

**kwargs
    Instructions on how to decorate your plots.
    The keyword arguments are passed to `matplotlib.axes.Axes.plot()` 

• If there are multiple possible targets, they are all listed (see below)
• If you happen to use some automation tool to interpolate and link your documentation, then you might list the possible keyword arguments in **kwargs for the convenience of the end users. This kind of approach is used in matplotlib, for example. (see below)

How and when document **kwargs (Numpydoc)

1) When to use **kwargs?

First thing to note here is that **kwargs should be used to pass arguments to underlying functions and methods. If the argument inside **kwargs would be used in the function (and not passed down), it should be written out as normal keyword argument, instead.

2) Where to put **kwargs decription?

The location of **kwargs description is in the Parameters section. Sometimes it is appropriate to list them in the Other Parameters section, but remember: Other Parameters should only be used if a function has a large number of keyword parameters, to prevent cluttering the Parameters section.

• matplotlib.axes.Axes.grid has **kwargs in Parameters section.
• matplotlib.axes.Axes.plot has **kwargs in Other Parameters section (reasoning probably to large number of keyword arguments).

3) Syntax for **kwargs decription

The syntax for the description for the **kwargs is, following Numpydoc styleguide

Parameters
----------
... (other lines)
**kwargs : sometype
     Some description on what the kwargs are
     used for.

or

Parameters
----------
... (other lines)
**kwargs
     Some description on what the kwargs are
     used for.

The one describing the type is more appropriate, as [source].

For the parameter types, be as precise as possible

One exception for this is for example when the **kwargs could be passed to one of many functions based on other parameter values, as in seaborn.kdeplot. Then, the line for the type would become too long for describing all the types and it would be cleaner to use a bullet point list, which also describes the conditions on when the **kwargs are forwarded to where. Eg.:

Parameters
----------
fill: bool or None
    If True, fill in the area under univariate density curves or between 
     bivariate contours. If None, the default depends on multiple.
**kwargs
    Other keyword arguments are passed to one of the following matplotlib 
    functions:

    * matplotlib.axes.Axes.plot() (univariate, fill=False),

    * matplotlib.axes.Axes.fill_between() (univariate, fill=True),

    * matplotlib.axes.Axes.contour() (bivariate, fill=False),

    * matplotlib.axes.contourf() (bivariate, fill=True).

You may also add listing of the valid keyword arguments in **kwargs like in matplotlib.axes.Axes.grid. Here is the interpolated python doc/text version:

Parameters
----------
... (other lines)
**kwargs : `.Line2D` properties
    Define the line properties of the grid, e.g.::

        grid(color='r', linestyle='-', linewidth=2)

    Valid keyword arguments are:

    Properties:
    agg_filter: a filter function, which takes a (m, n, 3) float array and a dpi value, and returns a (m, n, 3) array
    alpha: float or None
    animated: bool
    antialiased or aa: bool
    clip_box: `.Bbox`
    clip_on: bool
    clip_path: Patch or (Path, Transform) or None
    color or c: color
    contains: unknown
    dash_capstyle: {'butt', 'round', 'projecting'}
    dash_joinstyle: {'miter', '
    ... (more lines)

This is convenient for the user, but challenging for the developer. In matplotlib this kind of luxury is made possible with the automatization using some special documentation decorators and linking¹. Manual writing of allowed kwargs will surely become a code maintenance nightmare.

4) Notes related to **kwargs / Extended help

Some additional info about the **kwargs could be included in the Notes section. For example matplotlib.axes.Axes.plot discusses marker styles, line styles and colors in the Notes section. ^[2]

^[1] They use a @docstring.dedent_interpd decorator which pulls the meaning of the kwargs to the final docs. So that is happening in place of %(Line2D:kwdoc)s, for example.
^[2] See: help(ax.plot) where ax is instance of matplotlib.axes.Axes.

If you read further in the document you linked it looks like there's no one standard style:

Optional keyword parameters have default values, which are displayed as part of the function signature. They can also be detailed in the description:

Description of parameter `x` (the default is -1, which implies summation
over all axes).

When a parameter can only assume one of a fixed set of values, those values can be listed in braces, with the default appearing first:

order : {'C', 'F', 'A'}
    Description of `order`.

I would recommending picking a style for your own project and sticking to it.

If you want to use numpydoc style, one possible way would be:

def create_person(name=None, age=None, base_person=None):
    r"""A function to create a person.

    Using this function, a person can be created using
    either a combination of `name` and `age` or providing a `base_person`.

    Parameters
    ----------
    name : int [optional, default=None]
        The name of the person to be created. Leave this as None to create a person
        using the `base_person` keyword.
    age : int [optional, default=None]
        The age of the person to be created. Leave this as None to create a person
        using the `base_person` keyword. 
    base_person : instance of Person class [optional, default=None]
        If `age` and `name` are None, this keyword can be used to create a person
        from an instance of the `Person` class."""

Personally, I would create two different functions, one creating a person by name and age, and one using a base_person object. Internally they could call the function you provided with the correct caller signature. E.g:

def create_person_explicit(name, age):
    return(create_person(name=name, age=age)

def create_person_from_object(base_person):
    return(create_person(base_person=base_person)

It's a little hard to tell what exactly is the right solution for your exact problem as too much information is missing.