Corporate jet Captain reported descending below the minimum vectoring altitude. Captain states it was caused by similar call signs.

Narrative

After 2 or 3 calls and vectors with this controller; we were at an altitude of 3000 feet and heard [Callsign] XYZ called out descend to 2000 feet. Pilot not flying (PNF) called back [Callsign] 'XXZ' descend to 2;000 ft. And he set 2;000 feet in altitude selector. When we did not here a correction that our call back was wrong we descended to 2;000 ft. After starting down I asked PNF to call back on radio if that was for 'XXZ'; us and the PNF instead asked 'Approach did [Callsign] XXZ miss a radio call?' The controller said no. 30 seconds later the controller said 'XXZ' return to 3;000 feet. Minimum Safe Altitude he said was 2900 feet in that area!So at about 2;500 ft. I; Pilot flying went back up to 3;000 ft. MSL. After that we heard another call sign on the same frequency moments later with another different call sign that included [Callsign] 'XYZ'. We may have responded back at the precise time the other aircraft did and blocked out their response. When we heard nothing back in our supposed wrong response to altitude change; we descended to 2;000 ft. Shortly their after we did hear the controller giving instructions to a call sign different from ours with a different number after it. The controller mixed up us- Aircraft X with Aircraft Y as there was no other aircraft that I know on the frequency with us.