Q.Why is CC amplifier called emitter follower?

In a common-collector (CC) amplifier the input is applied between base and collector and the output is taken from the emitter, with the collector at AC ground. Because the emitter voltage closely follows the base voltage, it is universally called an emitter follower.

Working: on the positive half-cycle the forward bias increases, so $i_B$ and the emitter current $i_E = (1+\beta) i_B$ rise; the output across $R_E$ rises with the input, so input and output are in phase. The output voltage is $v_o = v_{in} - V_{BE}$; since $V_{BE}$ is small, $v_o \approx v_{in}$, giving a voltage gain just below 1 — the CC amplifier produces essentially no voltage amplification. …