Can you steal a user's identity if you gain their old domain name?

Just a random thought experiment. Let’s say I have my account on a lemmy instance: [email protected]. One day I decide to stop paying for the domain and move to [email protected], and someone else gains it and also starts up a lemmy instance.

If they make their own [email protected], how do federated instances distinguish who’s who?

Have I misunderstood the role of domain names in this?