It will only matter if the speed of the vehicle, aircraft, spacecraft or whatever is a significant proportion of the speed of the communication waves.
For sound (only a few hundred miles per hour) quite a low speed is easily detectable by our ears as a change in pitch.
For ocean waves, the effect can be quite extreme. Sailing downwind, a wave might catch up with you every minute or so, while sailing the other way at the same speed you might hit a dozen a minute -- their speed is very close to yours.
However, for radio waves (light-speed -- hundreds of millions of miles an hour) the speed of most things will cause such a small doppler shift it'll still appear to be the same frequency. Perhaps spacecraft do need some small adjustment, as their relative speed can be very high.