No, it's like giving someone a set of keys to your car, and they take it for a drive.

I think it’s more like you registered the car in their name. Now they’re allowed to use it, and also responsible for the thing which they didn’t want.

Consider that the “imposter” starts uploading child porn or something, and it’s on an account registered to your address. I think it’s perfectly A-OK to tell the service that it’s not me using the thing and I want them to close the account someone created in my name.