That said, with some custom programming, you might be able to detect multiple logins from the same computer by detecting their MAC address. In theory, these addresses are supposed to be unique across the world through it is possible to fake even this through software - a virtual machine for example.
I think the only possible option would facial or fingerprint recognition. Of course this wod require custom programming too however a cheap version of this might be to have users share their webcam and their screen with the teacher who would monitor activity in real time. Of course this is only feasible if you have a few students at a time or a lot of assistant teachers to do the monitoring.
Another option might be to make use of Proctors with AI to do the monitoring. I was just looking into it this last week for a client. Very interesting technology. This commercial technology actually exists today and several even have integrations for Moodle. Many of them guaranty no possible cheating.
Might be a problem for students without webcams though. Licensing is not cheap but it might be worth it to you depending on your circumstances.
Hope you find something helpful in all of this.
Best regards,
Michael Milette