Question

Neighbouring coil will induce a voltage in a coil termed as

Answer 1

The process is termed as Mutual Induction.

I don't think the voltage has any special name, maybe just induced voltage?

Answer 2

The core is often shaped as a square loop with primary and secondary coils wound on opposite sides. The construction of a transformer allows the magnetic flux generated by a current changing in one coil to induce a current in the neighboring coil.