Flight instructor with student on training flight reported a NMAC on final approach when the student misidentified the aircraft ATC had directed them to follow.

Narrative

I was in the pattern doing landings with my commercial student. There were 7 airplanes in the pattern at the same time. On one of the landings we were told to follow Aircraft Y and report in sight. My student pointed out and told ATC that she saw Aircraft Y on final. This was not Aircraft Y. Aircraft Y was #2 and we were #3. She turned us base and we were close to the final approach flight path of the real Aircraft Y. Immediately once I noticed a plane coming straight for us; I safely made a left turn to avoid collision. At the same time I was taking evasive action; tower told is to immediately turn left. I recognized them and said; 'turning left; we have the traffic in sight.' Under the situation; I remained calm and collected and took controls as the instructor on board of the aircraft should. Once I turned us out of the collision course of Aircraft Y; we re-entered the final leg.I have learned a lot from this experience. I will always check if final is clear and will not rely on another pilot saying that they have the aircraft in sight. I will also not rely on ATC saying which type of aircraft to follow because that is extremely hard to identify if you are not familiar with the aircraft in question or if they do not appear on the PFD ADS-B. Some communications I can do better as a pilot is to question ATC if I am questioning what number into the field I am. Another communication or system I have now understood the importance of is making sure final is clear; even at a towered airfield. Some suggestions I could make too ATC is being clearer with directions. With as many people in the pattern as there was; we should have been just told to extend downwind and they would call my base. I am not blaming tower because it was the responsibility of myself but if everyone worked as a team it would not have happened.