  The Noether symmetry approach is useful tool to restrict the arbitrariness in
a gravity theory when the equations of motion are underdetermined due to the
high number of functions to be determined in the ansatz. We consider two
scalar-coupled theories of gravity, one motivated by induced gravity, the other
more standard; in Bianchi I, Bianchi III and Kantowski-Sachs cosmological
models. For these models, we present a full set of Noether gauge symmetries,
which are more general than those obtained by the strict Noether symmetry
approach in our recent work. Some exact solutions are derived using the first
integrals corresponding to the obtained Noether gauge symmetries.
