We report an experimental implementation of dynamical holographic tweezers for single trapped atoms. The tweezers are realized with dynamical phase holograms displayed on the liquid crystal spatial light modulator. We experimentally demonstrate the possibility to trap and move single rubidium atoms with such dynamic potentials, and study its limitations. Our results suggest that high probability transfer of single atoms in the tweezers may be performed in large steps, much larger then the trap waist. We discuss intensity-flicker in holographic traps and techniques for its suppression. Loss and heating rates in dynamic tweezers are measured and no excess loss or heating is observed in comparison with static traps.