What is the following kind of equivalence relation between representations called?
Let $r_1: G \to GL(V)$ and $r_2: G \to GL(W)$ be two representations of group $G$. There is a group automorphism $a: G\to G$ and a vector space isomorphism $i: V\to W$, such that $$r_2(a(g)) (i(v))= i(r_1(g) (v))$$ for any $g\in G$ and $v\in V$.
(There are cases that $r_1$ and $r_2$ are equivalent in the above sense but are not equivalent representations; say, having two different, but equal up to an outer automorphism, characters).