If you're talking about an equivalent for C# before C#6, this will get the job done (in a hacky way) for properties. It can probably be expanded upon to include fields, methods, etc.

public static class TestExtension
{
    public static String nameof<T, TT>(this T obj, Expression<Func<T, TT>> propertyAccessor)
    {
        if (propertyAccessor.Body.NodeType == ExpressionType.MemberAccess)
        {
            var memberExpression = propertyAccessor.Body as MemberExpression;
            if (memberExpression == null)
                return null;
            return memberExpression.Member.Name;
        }
        return null;
    }
}

Just whipped this up quickly, so there's a lot to be improved, but you use it like this:

public class myClass
{
    public string myProp { get; set; }
}

var a = new myClass();
var result = a.nameof(b => b.myProp);

Result contains 'myProp'

Update:

More comprehensive (though still not that pretty)

public static class TestExtension
{
    public static String nameof<T, TT>(this Expression<Func<T, TT>> accessor)
    {
        return nameof(accessor.Body);
    }

    public static String nameof<T>(this Expression<Func<T>> accessor)
    {
        return nameof(accessor.Body);
    }

    public static String nameof<T, TT>(this T obj, Expression<Func<T, TT>> propertyAccessor)
    {
        return nameof(propertyAccessor.Body);
    }

    private static String nameof(Expression expression)
    {
        if (expression.NodeType == ExpressionType.MemberAccess)
        {
            var memberExpression = expression as MemberExpression;
            if (memberExpression == null)
                return null;
            return memberExpression.Member.Name;
        }
        return null;
    }
}

Accessing static properties/fields:

TestExtension.nameof(() => myClass.MyOtherField)

Accessing parameters within functions:

void func (int a) {
    TestExtension.nameof(() => a);
}

nameOf - Gets resolved at Compiletime - if you decompile, you will see that the compiler just translated the classname (without the Namespace(!)) into a constant string instead. So be aware!

If you want to get a classe's name use typeof() or GetType() to get the specific (maybe derived) type at Runtime and read the value of
the .Name-Property in .net < C#6.

Read more at MSDN

To my knowledge there are three options to not have to use a magic string

1. nameof which requires Visual Studio 2015 (But can be compiled to other versions of the .net framework)

   nameof(this.Property)
   

2. use a method that takes an expression and returns the property name as found in this post "Get string name of property using reflection"

   var propertyName = GetPropertyName(  
       () => myObject.AProperty); // returns "AProperty"
   

3. CallerMemberNameAttribute - (Only available in .net framework 4.5, included because original post said older versions like .net framework 4.0 which I guess includes 4.5) The draw back of this method is it is only useful when you need to string representation of the current method you are operating in.

   public string IsChecked  {
      set{
          Console.WriteLine(GetCurrentMemberName()); // prints "IsChecked"
      }
   }
   
   string GetCurrentMemberName([CallerMemberName] string memberName = "")
   {
        return memberName;
   }