In C# it is most common to either name the private variable _Name or m_Name. This also makes it easy to visually match up Properties because if you have a property Name, which uses a local private variable _Name, it is easy to see quickly what it is for.
Without the this keyword in your example, all you are doing is assigning the local variable to the local variable (and not to the private variable). Which is why it compiles, but won't do what you think it is doing.
