TRACON Controller missed a read back which led to the wrong aircraft taking an instruction resulting in a MVA error.

Narrative

Aircraft X was inbound direct to our satellite airport ZZZ from the East at FL150. When he checked on with me I told him to expect the Visual Approach into ZZZ and to descend and maintain FL120. The MVA he was flying over is FL112. The Pilot read the instructions back and I went back to focus on the sequence at ZZZ1. One of the aircraft in the Sequence was Aircraft Y; was instructed to fly present heading and descend and maintain FL100.Though I did not know it at the time; Aircraft X had taken the clearance issued to Aircraft Y. During that time there was multiple VFR pop ups; VFR overflights with conflicting traffic that I was dealing with and one IFR pickup in the air. Because my focus at the time was west of ZZZ1 airport and did not observe Aircraft X descending through FL120. When the Low Altitude Alert (LA) went off I issued the low altitude alert and climbed Aircraft X to FL120. The pilot questioned if we wanted him to climb because he was 'passed the ridge' I then issued him FL112 as it was the lowest I could assign. The MVA in the area was FL112 and Aircraft X and descended to FL101 before he started to climb again.Biggest factor in this event was the hearing and read back. There was even a moment that Aircraft Y asked me to restate the instructions which should have sent a red flag to me because I had heard the read back. I assumed he was just confirming the instructions not that he missed them and Aircraft X took the wrong instruction.