SR04 As only Transmitter and Receiver
I think this is the module that you are using. (please confirm - if it isn't I'll nuke this answer from orbit) The way that module works is that it sends a series of ultra sonic pulses , measures the distance from time of flight.  The sent pulse and the received pulse have to be related and timed.

A separate transmitter and receiver will not be linked together so the receiver will get very confused.

So in short you cannot do as you want to.

You also have the problem of steering, this unit tells distance only directly in front of it, you have no way of knowing if the person it is following has moved to the side and in which direction.

I think that an optical system that tracks along a horizontal angle that only tracks a specific wavelength or pulse pattern will give you both the identity and the direction (for steering) that you need.  Keep the US sensor to prevent the robot from running over the person of course.