Is there a word for the noun modified by an adjective?

A noun together with any complement to that noun is an N-bar, often written N', according to McCawley in "The Syntactic Phenomena of English". An example of a noun complement is "of the bride" in the N' "father of the bride". That's a preliminary to answering your question.

Now, here is how adjectives and other N'-modifiers fit in. An adjective combines with an N' to form another N' (consistent with McCawley's idea that modifiers do not change category). So "young father of the bride" has the structure [N' young [N' father PP] ], where "father" is a noun. With simply an adjective modifier but no noun complement, then, we have [N' young [N' [N father ] ] ].

Other N' modifiers, such as relative clauses are treated the same way as adjectives.

The antecedent in indefinite pronominalization for "one" is an N'. Thus a noun alone, a combination of noun and adjective, or a combination of noun and relative clause can be antecedent to "one". The determiner of a NP is outside the N' part, so the determiner is not part of the antecedent of an indefinite pronoun.

Your example with "him" requires a NP antecedent, not an N'.