The following is one of those sentences which always seem obscure to me.
The subject names the person, place, or thing being talked about.
I think being is used as verb and talked as an adjective in the above sentence. But if it were up to me then I would write that sentence as follows:
The subject names the person, place, or thing (that is)/(which is) being talked about.
Please give your answer in the light of English grammar.