Sort with one element at the end

  List<Car> sortedCars = cars
        .stream()
        .sorted(Comparator.comparing(
            Car::getName,
            Comparator.comparing((String x) -> x.equals("Unassigned"))
                      .thenComparing(Comparator.naturalOrder())))
        .collect(Collectors.toList());

There are a lot of things going on here. First I am using Comparator.comparing(Function, Comparator); then (String x) -> x.equals("Unassigned") which actually compares a Boolean (that is Comparable); then the fact that (String x) is used - as this type witness is used to correctly infer the types...

The most direct and and easy-to-read solution is probably to write a custom comparator that implements your sorting logic.

You can still use the Comparator.comparing method to make it a bit prettier, though:

public static final String UNASSIGNED = "Unassigned";

List<Car> cars = List.of(
    new Car("Unassigned"), 
    new Car("Nissan"), 
    new Car("Yamaha"), 
    new Car("Honda"));

List<Car> sortedCars = cars.stream()
    .sorted(Comparator.comparing(Car::getName, (name1, name2) -> {
            if (name1.equals(name2)) return 0;
            if (name1.equals(UNASSIGNED)) return 1;
            if (name2.equals(UNASSIGNED)) return -1;
            return name1.compareTo(name2);
    }))
    .collect(toList());

---

It is possible to extract the "at-the-end" functionality to a separate comparable combinator method. Like this:

List<Car> sortedCars = cars.stream()
    .sorted(Comparator.comparing(Car::getName, withValueAtEnd(UNASSIGNED)))
    .collect(toList());

public static <T extends Comparable<T>> Comparator<T> withValueAtEnd(T atEnd) {
  return withValueAtEnd(atEnd, Comparator.naturalOrder());
}

public static <T> Comparator<T> withValueAtEnd(T atEnd, Comparator<T> c) {
    return (a, b) -> {
        if (a.equals(atEnd)) return 1;
        if (b.equals(atEnd)) return -1;
        return c.compare(a, b);
    };
}

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Also, it's good style to use a named constant for special values like your "Unassigned".

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Also, note that if you don't need to keep the unsorted cars list, then you can sort that list in place instead of using a stream:

cars.sort(UNASSIGNED_COMPARATOR);

You could just replace "Unassigned" with an end-of-alphabet string in your comparator.

Comparator.comparing(car -> car.getName().equals("Unassigned") ? "ZZZ" : car.getName())