It is demonstrated that toroidicity (as well as ellipticity and other kinds of deviations of the magnetic configuration from the cylindrical geometry) can result in linear transformations of propagating kinetic Alfvén waves (KAWs) into other KAW branches, which differ by their mode numbers from the initial waves. Analytical expressions for the amplitudes of the transformed and non-transformed waves are derived. The transformation is found to be strong for waves with low poloidal mode numbers in typical present-day tokamaks. It may affect the mode numbers observed by external magnetic measurements and weaken the Landau damping of the waves, thus extending the region of the wave propagation.