  We determine the most general time-independent Noether symmetries of
two-field cosmological models with rotationally-invariant scalar manifold
metrics. In particular, we show that such models can have hidden symmetries,
which arise if and only if the scalar manifold metric has Gaussian curvature
$-3/8$, i.e. when the model is of elementary $\alpha$-attractor type with a
fixed value of the parameter $\alpha$. In this case, we find explicitly all
scalar potentials compatible with hidden Noether symmetries, thus classifying
all models of this type. We also discuss some implications of the corresponding
conserved quantity.
