YOu probably should add :
<datagridtemplatecolumn.>CellEditingTemplate>
<DataTemplate>
<TextBox Text={Binding Path=Model.Name, Mode=TwoWay} >
</DataTemplate>
</DataGridTemplateColumn.CellEditingTemplate></datagridtemplatecolumn.>
P.S
the DataGridTemplateColumn.CellTemplate should contain TextBlock