In your code sample, Person.Name is a field rather than a property. WPF data binding considers only properties, not fields, so you need to change Person.Name to be a property.
In the code shown you're setting ItemsSource twice, the first time in XAML (called by InitializeComponent) to the DataContext of ComboBox1, which can't be determined from what you've posted but it's probably not what you want. After that you're resetting it from code to your list object (here with typos). In this code you're also adding the same instance of Person 4 times and just changing its Name and ID over and over.
I suspect a combination of these issues and the fact that you're using a List instead of ObservableCollection are causing the issues in your application.
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