The doppler shift will change as the satellite transitions overhead, this is very clear if you look at a spectrum capture of the narroband beacons with a static LNB, and can be corrected by the user terminal, as it is expecting this shift and has software written specifically to deal with it.
In the case of e.g. LTE, a UE is not designed to cater for a changing doppler shift, so this is compensated by the satellite. In a theoretical MIMO configuration where multipath is achieved by using beams from multiple satellites towards a UE’s location, the signals such as P-SS and S-SS from each satellite would arrive at the UE at different times, frequencies, and power levels.
Here is an interesting paper that discusses the topic:
https://arxiv.org/pdf/1706.06013