  We study Noether symmetries in two-field cosmological $\alpha$-attractors,
investigating the case when the scalar manifold is an elementary hyperbolic
surface. This encompasses and generalizes the case of the Poincare disk. We
solve the conditions for the existence of a `separated' Noether symmetry and
find the form of the scalar potential compatible with such, for any elementary
hyperbolic surface. For this class of symmetries, we find that the
$\alpha$-parameter must have a fixed value. Using those Noether symmetries, we
also obtain many exact solutions of the equations of motion of these models,
which were studied previously with numerical methods.
