 Solution

Use a non-dummy circular linked list with a pointer to its last node:

private var last: Node = null

Null represents the empty book. In a nonempty book, last.next is the first node, and following next makes one finite simple cycle containing last. Names are unique around that cycle. This representation makes appending a new entry constant-time once a failed name search has established absence. The abstraction function collects every name/number pair on one complete turn of the cycle, rather than following pointers until null.