random elements from a list DURING the addition

There are 20 names in my code. my function has 2 options to add elements to a list I've:

1.

Inserting all the 20 names to the list:

public void addNames() {
    list.add("name1");
    list.add("name2");
    ...
    list.add("name20");
}

2.

Adding only 5 random names(from the 20 names) to the list. For doing it, I thought about 2 ways. What's the best way to random 5 names from the 20? maybe you have a better way.

A.

Using a random set of indices (each value will be between 0 to 19 because there are 20 names) and before the 'add' I'll check if adding them or not by some counter:

public void addNames() {
    // adding 5 random indices between 0 to 19 to the set
    Set<Integer> set = new HashSet<Integer>();
    Random r = new Random();
    Set<Integer> indices = new HashSet<>(numRandomNames); //==5
    for (int i = 0; i < numRandomNames; ++i) {
        int index = r.nextInt(numNames - 0); //==19
        indices.add(index);
    }

    int counter = 0;
    if (indices.contains(counter)) {
        list.add("name1");
    }
    counter++;
    if (indices.contains(counter)) {
        list.add("name2");
    }
    counter++;
    if (indices.contains(counter)) {
        list.add("name3");
    }
    ...
}

B.

RandomList that extends List and overrides the 'add' function to do the same as 'A.' does BUT the override 'add' will decide whether adding the value inside the function so my function will look the same as 1. with the override 'add' function

Do you think about a better solution? if not, then which one is better? (A or B?). I just saw that people recommends not to extend the java collection but I think it's the best solution from these 2 solutions.

NOTE

====

my code can have 10000 names or more even so I don't want to add all the 10,000 names to this\other list and then random 5 of them to other list. I prefer to do it DURING the addition in order to avoid many places of the list while I don't really need them.