Is there a standard way to define a formal language transformer?
Without knowing what kind of transformation you compute, it's unlikely that there's a useful word. Assuming that any two inputs are processed independently of each other, you're looking at (computable) function(al)s from $A^* \to B^*$ with two alphabets $A$ and $B$.

Here are some specific kinds of transformations:


string homomorphisms,
finite-state transduction, or
the transducer equivalent(s) of any automaton model.