In reading any classical description of the ‘Doppler Effect’ the question of the energy of a photon is never discussed.
The energy of a photon is E=hv. Where h = Planck constant and v = frequency. Ignoring Planck constant we can simply say the energy of a photon is equal to its frequency.
The ‘Doppler Effect’ states that the measured frequency of light at a receiver will be altered by the motion of the source or the receiver.
I can then rewrite the ‘Doppler Effect’ to read the measured energy of a photon will be altered by the motion of the source or receiver.