UPDATE: The feature described here was added to C# 7.
The feature you want is called "ref locals" and it is not supported in C#.
The CLR does support generating code that contains ref locals, and a few years ago I wrote an experimental version of C# that had the feature you want, just to see if it would work. You could do something like:
Person a = whatever;
ref Person b = ref a;
and then as you say, changes to "b" would change the contents of "a". The two variables become aliases for the same storage location.
Though it was a nice little feature and worked well, we decided to not take it for C#. It's possible that it could still happen in a hypothetical future version of the language, but I would not get all excited about it in expectation; it will probably not happen.
(Remember, all of Eric's musings about hypothetical future versions of any Microsoft product are For Entertainment Purposes Only.)