Is the Doppler radar the only satellite radar in the world?

Actually the Doppler Radar aka nexrad Next generation radar is not a satellite it is a radar. Satellites are floating around the world in space and Doppler radars are here on earth to monitor weather. As far as I know the Doppler radar is the only weather radar in the world. It is basically the only thing used for monitoring weather.

I the above is not quite correct. Weather radars come in two basic types coherent and non-coherent. The Coherent radar come in Doppler Radar which can be FMCW or Active Pulse Doppler. The non coherent Pulse Radar merely aim high energy pulses at the clouds and display the returned power in a colour display. The coherent version integrates many pulses together to gain a Higher signal to Noise and to detect water drops moving in clouds. That aside, to answer the question which has nothing to do with weather radar, Doppler radar is frequency used in space verticals because its coherent processing gains in achieves help to offset the ranges it operates over, but it is not the only radar technique to be used on satellites and it depends on what the radar is trying achieve. Note that Doppler radar is non a synonymous exclusively of "nexrad Next generation radar".