IPv6 has two main types of non-broadcast addresses to think about: link-local (fe80::) and public.
A device can self-assign a link-local address, but it only provides direct access to other devices connected to the same physical network. This would be used for peer discovery, such as asking every device if they are capable of acting as a router.
Once it finds the router, there are two ways it can get an IP address that can reach the wider internet: SLAAC and DHCPv6. SLAAC involves the device picking its own unique address from the block of addresses the router advertises itself as owning, which is likely what you’re concerned about. One option for ensuring a device can’t just pick a different address and pretend to be a new device is by giving it a subset of the router’s full public address space to work with, so no matter what address it picks, it always picks something within a range exclusively assigned to it.
Edit: I butchered the explanation by tying to simplify it. Rewrote it to try again.