class PeopleViewModel
    {
        public ICollectionView SearchPeopleView { get; private set; }
        public ObservableCollection<SearchPerson> SearchPeople { get; private set; }

        private string _searchString = "";

        public string SearchString
        {
            get { return _searchString; }
            set
            {
                _searchString = value;
                SearchPeopleView.Refresh();
            }
        }


        public PeopleViewModel()
        {
            SearchPeople = MockData();
            SearchPeopleView = CollectionViewSource.GetDefaultView(SearchPeople) as CollectionView;
            SearchPeopleView.Filter = ViewFilter;
        }


        private ObservableCollection<SearchPerson> MockData()
        {
            return new ObservableCollection<SearchPerson>(
                Enumerable.Range(1, 10000)
                           .Select(i => new SearchPerson() { FullName = $"{i} name" }));
        }

        private bool ViewFilter(object obj)
        {
            var user = obj as SearchPerson;
            return user != null && user.FullName.Contains(_searchString);
        }
    }


    class SearchPerson
    {
        public string FullName { get; set; }
    }

/*
<!-- Xaml -->
<Window x:Class="WpfApp1.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"
        mc:Ignorable="d"
        Title="MainWindow" Height="350" Width="525">
    <DockPanel LastChildFill="True">
        <TextBox DockPanel.Dock="Top" Text="{Binding SearchString, UpdateSourceTrigger=PropertyChanged, Delay=50}"/>
        <DataGrid
            ItemsSource="{Binding SearchPeopleView}">
            <DataGrid.Columns>
                <DataGridTextColumn Binding="{Binding FullName}" Width="*"/>
            </DataGrid.Columns>
        </DataGrid>
    </DockPanel>
</Window>
*/