Thanks for the patch, it looks good, I have 2 remarks though:

- "under the name name" could be replaced by "under the given name".

- "The *search_function*'s refcount is incremented by this function."
This information is not useful to the caller - she just wants to know whether she still owns the reference she had before.  Most probably here, the refcount is incremented because the object is stored in a list; the caller still owns the reference to the parameter, like most functions of the API, and there is nothing to say about refcounts here.