Why was "name" used here? and if I start the sentence with "what is the one thing", would the meaning be the same?
"Name" here is being used as a verb meaning to specify something that you desire. You could change the start of the sentence to your suggestion of "what is the one thing", without affecting the meaning or nuance. Ex: Name the one food you could eat for the rest of your life. Ex: What is the one food you could eat for the rest of your life?