Problems when printing a circular singly linked list

I have a circular singly linked list code:

class Node{
    constructor(value){
        this.value = value;
        this.next = null;
    }
}

class LinkdeList{
    constructor(){
        this.first = null;
        this.last = null;
    }

    empty(){
        return this.first === null
    }

    insert(value){
        let newest = new Node(value);

        if (this.empty()) {
            this.first = this.last = newest;
            this.last.next = this.first;
        }else{
            newest.next = this.first;
            this.first = newest;
            this.last.next = this.first;
        }
    }

    traverse(){
        let aux = this.first;
        while (aux.next != this.first) {
            console.log(aux.value);
            aux = aux.next;
        }
    }
}

let linked = new LinkdeList();
linked.insert("David");
linked.insert("John");
linked.insert("Adam")
linked.insert("Bob");
linked.traverse();

And when I tried to print the list, I just get in console 3 names:

Bob
Adam
John

And as you can see I push 4 names in my linked list. I tried to print the values of my list in the traverse method, but It didn´t work because I don´t get in console:

Bob
Adam
John
David

Solution

The loop stops one step too early. This is a good case for a do ... while loop. You should also protect it from failing when the list is empty

    traverse() {
        if (this.empty()) return; // <---
        let aux = this.first;
        do {
            console.log(aux.value);
            aux = aux.next;
        } while (aux != this.first);
    }

Some other remarks on your code:

As in a non-empty circular list it is always true that the head follows after the tail, it is actually not needed to maintain a first reference. Just keep a last reference, knowing that you can always get the head of the list via last.next.
console.log should not be used in a class method for anything else than debugging. Give your traverse method more flexibility by making it a generator. That way you leave the decision of what to do with the values to the caller of that method.
As in a circular list a node should never have a next property with a null value, don't assign null in the Node constructor. Instead give it a self-reference.
Name the empty method isEmpty as it more clearly indicates that this will not empty the list, but will return whether it is empty.
Fix a typo in the class name: LinkedList

class Node {
    constructor(value) {
        this.value = value;
        this.next = this; // self-reference
    }
}

class LinkedList {
    constructor() {
        this.last = null; // No need for a `first`
    }

    isEmpty() {
        return this.last === null;
    }

    insert(value) {
        const newest = new Node(value);
        if (!this.isEmpty()) {
            newest.next = this.last.next;
            this.last.next = newest;
        }
        this.last = newest;
    }

    *traverse() { // Generator
        if (this.isEmpty()) return; // Guard
        let aux = this.last;
        do  {
            aux = aux.next;
            yield aux.value; // Don't print. Yield instead.
        } while (aux != this.last);
    }
}

const linked = new LinkedList();
linked.insert("David");
linked.insert("John");
linked.insert("Adam")
linked.insert("Bob");
// Caller of traverse can decide what to do: we want to print:
for (const name of linked.traverse()) console.log(name);