What does it mean to be a nameless flower+a happy puppy?

Being a nameless flower+being a happy puppy means that you don't have to grow up according to the prescribed trajectory, do what you want to do and become the person you want to be. To be a nameless flower here is to grow up carefree; Be a happy puppy, especially the person you want to be. Therefore, being a nameless flower+being a happy puppy together means that you don't have to grow up according to the prescribed trajectory, do what you want to do and become the person you want to be.