We extend the study of inverse boundary value problems for quasilinear anisotropic conductivities from Euclidean domains to compact Riemannian manifolds with boundary. Given boundary voltage and current measurements, represented by the Dirichlet-to-Neumann (DN) map, we investigate whether the quasilinear anisotropic conductivity can be uniquely determined. Our main result establishes uniqueness for quasilinear anisotropic conductivities, where the conductivity tensor is given by a scalar function multiplied by a fixed Riemannian metric. Under natural geometric conditions, such as conformal flatness or boundary rigidity of the underlying manifold, we show that this scalar factor can be uniquely determined from the boundary measurements.