Postgresql 9.4: How to find out the stack level of nested function

There's a different, simpler, solution for this. Add an argument to function fA with a default value, for instance: called_from_b BOOLEAN DEFAULT FALSE. Then, provide that argument when calling fA from fB.

I understand that this doesn't directly answer your question, but it does provide a solution for the example usecase that you provide.

As of 2022, this is now possible (and easy) in all currently supported PostgreSQL versions, thanks to GET DIAGNOSTICS:

BEGIN TRANSACTION;

CREATE TYPE stuff AS (
    nestlevel int
    ,arbitrary text
);

CREATE OR REPLACE FUNCTION fa()
    RETURNS stuff
    LANGUAGE plpgsql
    AS $$
DECLARE
  _stack text;
BEGIN
    GET DIAGNOSTICS _stack = PG_CONTEXT;

    RETURN ROW(
        array_length(string_to_array(_stack, E'\n'), 1) - 1,
        'Some text'
    )::stuff;
END;
$$;

CREATE OR REPLACE FUNCTION fb()
    RETURNS stuff
    LANGUAGE plpgsql
    AS $$
BEGIN
    RETURN fa();
END;
$$;

SELECT fa();
SELECT fb();

ROLLBACK TRANSACTION;

BEGIN
CREATE TYPE
CREATE FUNCTION
CREATE FUNCTION
       fa
-----------------
 (0,"Some text")
(1 row)

       fb
-----------------
 (1,"Some text")
(1 row)

ROLLBACK