How to sequentially call a custom function with a new parameter (postresql)?

Question

PostgreSQL

The problem is the following.
I wrote my own function, it takes 1 parameter as input,

I want to do something like

SELECT
DISTINCT C.city_nm
,N.Name
FROM city C
INNER JOIN (SELECT city_nm, name FROM my_func(C.city_nm)) N
USING (city_nm)

Naturally, nothing comes out of the output
HINT: There is an entry for table "C", but it cannot be referenced from this part of the query.

How can you organize a sequential function call with a unique list of parameters?