General term for map/fmap
In addition to being in agreement with Derek (that the ana/cata terminology doesn't bring much to the table) I'll note that the "category theoretic" terminology for the general map function of type
$$\mathrm{map}:\forall \alpha\beta. (\alpha \rightarrow\beta)\rightarrow(F\ \alpha\rightarrow F\beta) $$
for a functor $F$ is simply "the functorial action of $F$", and is often written as $F$! For example, on lists, map f l would be written $\mathrm{List}(f)(l)$.

For some reason, computer scientists seem to prefer to have a seperate name for the type constructor and the action on morphisms, but mathematicians do not really consider non-functorial constructors anyways.