When you register to vote, you give your address as well as proof of eligibility to vote. That address is used to assign you a polling place, and also as an additional piece of data needed in order to filter out fakers. Your voting eligibility is checked before being added to the list, which also mitigates fakers.

If you're trying to register in someone else's name, you have to pray that they don't register themselves or show up to the polls to vote. That's a gamble which prevents systematic individual voter fraud.

So... For each election, I have to register anew and the agency in charge has a backoffice is cross-checking this against... something? I guess they would first look if I was voting the last time? What if my birth certificate or whatever is from a different place. Do they assume I'm not risking using a forgery over politics (it's a fair assumption I would say)?