Doppler frequency when down-converting a receiving signal
When there is relative motion between the transmitter and receiver the frequency seen by the receiver is not $F_c$, so let's say you incur a Doppler shift of $\Delta_f$, then the shifted signal frqeuency is $F_c - \Delta _f$ now when you downconvert with $F_c$ the frequency offset of $\Delta_f$ still remains in the signal. That means the baseband spectrum "centred around freqeuency" of $0$ will be shifted by this value

In the receivers, this offset is estimated by the baseband signal processing (by performing correlation of time domain samples, linear shift in freqeuency domain means phase shift in time domain, so these correlations of samples simply leave the phase corresponding to the frequency offset due to doppler), there are other methods as well. Once these are estimated the clock at the receiver is further corrected with the estimation to tune the receiver to the "seen" signal freqeuency. So that the baseband spectrum is again centred around $0$ frequency