When you name a device, LastPass should remember that given name even once signing you out. If it has the same device unique identifier, why would you not auto-fill with the previously entered name?
Retyping my device name once a month means I stop doing it, which lowers total security (pic below shows how silly it is).
Why not also store the devices unique identifier in trusted devices and the last few IP addresses? If someone can write ANYTHING into a device name box, then it's trivial to pretend one device is another.