Surname for first name?

So our daughter is constantly calling baby brother "baby Sullivan" - and at first I was like "no no - that won't be his name" but it's growing on me. Am I crazy? Hahah.. I know it's typically a surname, and maybe it's just cause she calls him it all the time, but seriously I'm over here like "Sullivan. Sullivan. Sullivan" 
First and middle name would be Sullivan Lee