  We present three-dimensional, hybrid-kinetic numerical simulations of driven
Alfv\'{e}n-wave turbulence of relevance to the collisionless near-Earth solar
wind. Special attention is paid to the spectral transition that occurs near the
ion-Larmor scale and to the origins of preferential perpendicular ion heating
and of non-thermal wings in the parallel distribution function. Several novel
diagnostics are used to show that the ion heating rate increases as the
kinetic-Alfv\'{e}n-wave fluctuations, which comprise the majority of the
sub-ion-Larmor turbulent cascade, attain near-ion-cyclotron frequencies. We
find that ${\approx}75$-$80\%$ of the cascade energy goes into heating the
ions, broadly consistent with the near-Earth solar wind. This heating is
accompanied by clear velocity-space signatures in the particle energization
rates and the distribution functions, including a flattened core in the
perpendicular-velocity distribution and non-Maxwellian wings in the
parallel-velocity distribution. The latter are attributed to transit-time
damping and the pitch-angle scattering of perpendicularly heated particles into
the parallel direction. Accompanying these features is a steepening of the
spectral index of sub-ion-Larmor magnetic-field fluctuations beyond the
canonical $-2.8$, as field energy is transferred to thermal energy. These
predictions may be tested by measurements in the near-Earth solar wind.
