Pre C# 6.0 solution
You can use this to get a name of any provided member:
public static class MemberInfoGetting
{
    public static string GetMemberName<T>(Expression<Func<T>> memberExpression)
    {
        MemberExpression expressionBody = (MemberExpression)memberExpression.Body;
        return expressionBody.Member.Name;
    }
}
To get name of a variable:
string testVariable = "value";
string nameOfTestVariable = MemberInfoGetting.GetMemberName(() => testVariable);
To get name of a parameter:
public class TestClass
{
    public void TestMethod(string param1, string param2)
    {
        string nameOfParam1 = MemberInfoGetting.GetMemberName(() => param1);
    }
}
C# 6.0 and higher solution
You can use the nameof operator for parameters, variables and properties alike:
string testVariable = "value";
string nameOfTestVariable = nameof(testVariable);