In proton therapy, the prompt-γ (PG) radiation produced by the interactions between protons and matter is related to the range of the beam in the patient. Tomographic Compton imaging is currently studied to establish a PG image and verify the treatment. However the quality of the reconstructed images depends on a number of factors such as the volume attenuation, the spatial and energy resolutions of the detectors, incomplete absorptions of high energy photons and noise from other particles reaching the camera. The impact of all these factors was not assessed in details. In this paper we investigate the influence of the PG energy spectrum on the reconstructed images. To this aim, we describe the process from the Monte Carlo simulation of the proton irradiation, through the Compton imaging of the PG distribution, up to the image reconstruction with a statistical MLEM method. We identify specific PG energy windows that are more relevant to detect discrepancies with the treatment plan. We find that for the simulated Compton device, the incomplete absorption of the photons with energy above about 2 MeV prevents the observation of the PG distributions at specific energies. It also leads to blurred images and smooths the distal slope of the 1D PG profiles obtained as projections on the central beam axis. We show that a selection of the events produced by γ photons having deposited almost all their energy in the camera allows to largely improve the images, a result that emphasizes the importance of the choice of the detector. However, this initial-energy-based selection is not accessible in practice. We then propose a method to estimate the range of the PG profile both for specific deposited-energy windows and for the full spectrum emission. The method relies on two parameters. We use a learning approach for their estimation and we show that it allows to detect few millimeter shifts of the PG profiles.