Function first_name and last_name coursera

I am stuck with my code on my assestment. I have passed with sufficient score but I dont like to leave any question on fail- for my own learning. I manaed to get all statements, apart from the last one, where if first and last name are black, the output should be empty. But I am still getting Name - this word shoul dnot be there at all.

Thanks a lot!

   # code goes here
 if len(first_name)==0:
   string="Name: "+last_name
   
 elif len(last_name)==0:
   string="Name: "+first_name

 elif len(last_name)==0 and len(first_name)==0:
   string=""    

 else:
   string="Name: "+last_name+", "+first_name

 return string 

print(format_name("Ernest", "Hemingway"))
# Should return the string "Name: Hemingway, Ernest"

print(format_name("", "Madonna"))
# Should return the string "Name: Madonna"

print(format_name("Voltaire", ""))
# Should return the string "Name: Voltaire"

print(format_name("", ""))
# Should return an empty string

Name: Hemingway, Ernest
Name: Madonna
Name: Voltaire
Name: