What is the name of the device that sense the current flowing

Ampermeter

Explanation:

An ampermeter is a device that allows measuring an electron flow through a wire.

His main operation principle is to generate a magnetic field on a coil, which then is converted to an electric potential or voltage to be compared with a voltage reference, producing there a measurable value.

There are 2 types of ampermeters one is the standard form, which is a clamp that surrounds a wire and measures without changing/touching the circuit. The other one uses to terminals and it's required to open the circuit and make the current flow go through the ampermeter.