Changing the current in one coil induces EMF in another one, this phenomenon is called
Mutual induction
Mutual induction is the phenomenon of an emf being induced in one coil in response to current changing in another coil. This is the working principle of a transformer.
When an emf is produced in a coil because of the change in current in a coupled coil, the effect is called mutual inductance. The emf is described by Faraday's law and it's direction always opposes the change in the magnetic field produced in it by the coupled coil.