We analyze time-independent Noether symmetries of two-field cosmological models with rotationally-invariant scalar manifold metrics and notice that they decompose as direct sums of "visible" and "hidden" symmetries. The latter are determined by a generating function which satisfies the Hesse equation and arise if and only if the scalar manifold metric has a certain negative Gaussian curvature, i.e. when the model is of alpha-attractor type. We find the scalar potentials compatible with these symmetries.