The people who named it “quantum teleportation” had in mind Star Trek teleporters which work by “scanning” the object, destroying it, and then beaming the scanned information to another location where it is then reconstructed.

Quantum teleportation is basically an algorithm that performs a destructive measurement (kind of like “scanning”) of the quantum state of one qubit and then sends the information over a classical communication channel (could even be a beam if you wanted) to another party which can then use that information to reconstruct the quantum state on another qubit.

The point is that there is still the “beaming” step, i.e. you still have to send the measurement information over a classical channel, which cannot exceed the speed of light.