C# Custom getter/setter without private variable

Question

I learned c# recently, so when I learned to write properties, I was taught to do it like this:

public string Name { get; set; }

Auto properties

Answer 1

The answer is No, you cannot do that. It is because of recursion. (See line numbers 9 and 7):

Line 1  :   public string Name
Line 2  :   {
Line 3  :     get
Line 4  :     {
Line 5  :         return FirstName + " "  + LastName;
Line 6  :     }
Line 7  :     set
Line 8  :     {
Line 9  :         Name = value; // <-- Goes back to Line 7
Line 10 :     }
Line 11 :   }