Wifi Names disappearing and appearing with names of family members

Hello Friends, I am facing issues with my internet services. Internet service provider changed the modem multiple times but issue not resolved. When using Modem of brand A – after working for almost 15 – 20 min, wifi name getting change to wifi names with the names of my family members. When using other brand – its having same issue but after few hours ( 10 – 15 hours or more) . Even with PLUG AND PLAY services from different service provider ( with Data SIM) also getting disconnect after some time and wifi names with names of family members are showing. Can someone please advise what can be the root cause of this issue and how to get this fix ?