Is there any C# naming convention for a variable used in a property?

Per Microsoft's naming conventions, the proper way would be:

private string fubar;
public string Fubar { get { return fubar; } set { fubar = value; } }

However, many people prefer to prefix the private field with an underscore to help minimize the possibility of miscapitalizing and using the field when they meant to use the property, or vice versa.

Thus, it's common to see:

private string _fubar;
public string Fubar { get { return _fubar; } set { _fubar = value; } }

The approach you take is ultimately up to you. StyleCop will enforce the former by default, whereas ReSharper will enforce the latter.

In C# 6, there is new syntax for declaring default values for properties or making read-only properties, lessening the need for properties with backing fields that don't have any special additional logic in the get and set methods. You can simply write:

public string Fubar { get; set; } = "Default Value";

or

public string Fubar { get; } = "Read-only Value";

prefix the private with an underscore _Fubar

If you name your private variables starting with lower case, you can right click on them and have VS generate your getter/setter code for you;

Refactor->Enacpsulate Field...

It will name the property with Caps.