Can you "Renew"

I meant, Do I have to delete my previous one then get another one?

According to the page, they "disappear" after they expire. You can own multiple mini pets, though, so if your worry is being able to get another, yes you can.

I think he means is it autodeleted or does he like need to delete it then wait until 7AM to make a new one with the same name.

You can't even name them, so there's no worry about whether or not they disappear or require to be deleted.

You can buy as many whistles as you want, but can only have around 80 characters & pets at once.