There's a type for that in vavr, and it's called Option. You can return Option.none() in case there is no error, and return Option.some(errorMessage) in case there is an error.
If you still want to use Either, I would recommend to use the left side for errors and the right side for values (the happy path), because Either is right biased, so the map and flatMap methods act on Either only if it's a right value. In your case, since there's no value to return (i.e. a void), you can use Either<String, Void>, and return Either.right(null) for the success case, since null is the only inhabitant of the type Void (null is inhabitant of all non-primitive types in Java, as of now, unfortunately).
Or you could introduce a new type called Unit with a single inhabitant (i.e. a singleton), use Either<String, Unit> for your return type and return Either.right(Unit.instance()) to signal the lack of meaningful return value and avoid returning null values, because returning null values is kind of ugly.