Google has not made any official assertions. Of course changing the name of a product that is familiar to the user is not a one-way, one-way job, and Home Mini or Home Max does not yet have their "new name". However, it can be seen that Google is slowly applying changes to its existing product lines to create a "synchronization" with products that will be developed in the future.
In addition, the move also shows that Google does not wait to integrate new technology into its products and then rename them, which most other brands often do. In the future we may see the name 'Nest' everywhere, even if the device has nothing to change (except for the name, of course).