Bind the selected string in a TextBlock inside a ListView inside a cell of a DataGrid to a ViewModel

FodyWeaver.xml

<?xml version="1.0" encoding="utf-8" ?>
<Weavers>
  <PropertyChanged />
</Weavers>

MainWindow.xaml

<Window x:Class="WpfTest.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:WpfTest"
        mc:Ignorable="d"
        Title="MainWindow" Height="350" Width="525">

    <Window.DataContext>
        <local:ViewModel />
    </Window.DataContext>

    <Grid>
        <DataGrid ItemsSource="{Binding Rows}" AutoGenerateColumns="False" >
            <DataGrid.Columns>
                
                <!-- ID -->
                <DataGridTextColumn Header="ID" Binding="{Binding ID}" />
                
                <!-- List with names -->
                <DataGridTemplateColumn Header="Names">
                    <DataGridTemplateColumn.CellTemplate>
                        <DataTemplate>
                            <ListView ItemsSource="{Binding Names}">
                                <ListView.ItemTemplate>
                                    <DataTemplate>
                                        <DockPanel LastChildFill="True">
                                            <Button Content="Change" DockPanel.Dock="Right" Command="{Binding Path=DataContext.ChangeNameButton, RelativeSource={RelativeSource FindAncestor, AncestorType={x:Type DataGrid}}}" />
                                            <TextBlock Text="{Binding}" Margin="0,0,3,0" DockPanel.Dock="Left"/>
                                        </DockPanel>
                                    </DataTemplate>
                                </ListView.ItemTemplate>
                            </ListView>
                        </DataTemplate>
                    </DataGridTemplateColumn.CellTemplate>
                </DataGridTemplateColumn>
                
            </DataGrid.Columns>
        </DataGrid>
    </Grid>
</Window>

MainWindows.xaml.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;

namespace WpfTest
{
    /// <summary>
    /// Interaction logic for MainWindow.xaml
    /// </summary>
    public partial class MainWindow : Window
    {
        public MainWindow()
        {
            InitializeComponent();

            // Some data to work with.
            var model1 = new Model();
            model1.ID = 5;
            model1.Names.Add("Name1");
            model1.Names.Add("Name2");

            var model2 = new Model();
            model2.ID = 2;
            model2.Names.Add("NameA");
            model2.Names.Add("NameB");
            model2.Names.Add("NameC");

            // Setup ViewModel and View.
            var vm = this.DataContext as ViewModel;
            vm.Rows.Add(model1);
            vm.Rows.Add(model2);
            vm.ChangeNameButton.Callback = ChangeName;
        }

        public void ChangeName()
        {
            var vm = this.DataContext as ViewModel;
            Console.WriteLine($"Current selected name is: {vm.SelectedName}");
            vm.SelectedName = "Some other name";
        }
    }


    public class Model
    {
        public int ID { get; set; }
        public System.Collections.ObjectModel.ObservableCollection<string> Names { get; set; }

        public Model()
        {
            Names = new System.Collections.ObjectModel.ObservableCollection<string>();
        }
    }

    public class Btn : ICommand
    {
        public event EventHandler CanExecuteChanged;
        public Action Callback { get; set; }

        public bool CanExecute(object parameter)
        {
            return true;
        }

        public void Execute(object parameter)
        {
            Callback();
        }
    }

    [PropertyChanged.AddINotifyPropertyChangedInterface]
    public class ViewModel
    {
        public System.Collections.ObjectModel.ObservableCollection<Model> Rows { get; set; }
        public Btn ChangeNameButton { get; set; }
        public string SelectedName { get; set; }

        public ViewModel()
        {
            Rows = new System.Collections.ObjectModel.ObservableCollection<Model>();
            ChangeNameButton = new Btn();
        }
    }
}