General

Pet appreciation hot day question

So I need to know for today's hot day:
If I pick up the penguin pet in one world can I get the name tag in another? Or is it all in one box?

I want to name my tiger in Khaini but the opportunity to get a water of life-able penguin in reboot for free is almost too much to pass (jk it is) for someone who doesn't buy NX.

Thanks for your help