Not an expert. But there are a few ways to look at this.

Bodies that are in stable orbit can have only a specific velocity which is a function of its distance from & mass of whatever it is orbiting. So orbiting satellite's speed can be inferred from its orbital height.

There are ground based tracking stations that can technically measure the speed of any orbiting body.

Also read somewhere that LEO satellites could use GPS receivers to get a fix on their position. measuring change in this position also gives velocity. There a bunch of limiting conditions around max-height and velocity for this to work though.