What is the name of the situation when an object contains references to its previous and next elements in the chain?

This situation is called a doubly linked list. In a doubly linked list, each element (node) contains a reference to the previous and next elements, which allows efficient traversal in both directions along the chain.

Example of a doubly linked list node in Java:

class Node {
    int data;
    Node prev;
    Node next;

    Node(int data) {
        this.data = data;
        this.prev = null;
        this.next = null;
    }
}