Using IValueconverter

public partial class MainPage : UserControl
    {
        public MainPage()
        {
            InitializeComponent();
            bind();
           
        }

        private void bind()
        {
            SampleData obj = new SampleData();
            var m=obj.SampleData1();
            dgClientIssueEntryMain.ItemsSource = m;
        }
        public class Person
        {
            public string Name { get; set; }
            public int id { get; set; }
        }

        public class SampleData
        {
            public List<Person> SampleData1()
            {
                List<Person> people = new List<Person>();
                people.Add(new Person() { Name = "Jack Sparrow" ,id=1});
                people.Add(new Person() { Name = "William Turner", id = 2 });
                people.Add(new Person() { Name = "Davi Jones", id = 3 });
                people.Add(new Person() { Name = "Barbossa", id = 4 });
                people.Add(new Person() { Name = "Maggie", id = 5 });

                return people;
            }
        }

First I am creating one converter class

public object Convert(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
        {
            string Flag = (string)value;
            if (Flag == "Jack Sparrow")
            {
                return new SolidColorBrush(Colors.Green);
            }
            else if (Flag == "William Turner")
            {
                return new SolidColorBrush(Colors.Red);
            }
            else if (Flag == "Davi Jones")
            {
                return new SolidColorBrush(Colors.Purple);
            }
            else if (Flag == "Barbossa")
            {
                return new SolidColorBrush(Colors.Orange);
            }
            else
            {
                return new SolidColorBrush(Colors.Blue);
            }
        }

        public object ConvertBack(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
        {
            throw new NotImplementedException();
        }

My XAML Page

1.First you need to add reference of converter in usercontrol.

 xmlns:convert="clr-namespace:Usingconverter"

<UserControl.Resources>
        <convert:converter x:Key="converter" ></convert:converter></UserControl.Resources>

2.Bind Data in Control and pass Converter to convert and get back Background Color.

<Grid x:Name="LayoutRoot" Background="White">
           
        <sdk:DataGrid x:Name="dgClientIssueEntryMain" AutoGenerateColumns="False" VerticalAlignment="Center" IsReadOnly="True" HorizontalAlignment="Center"
                      Height="Auto" Width="Auto">
           <sdk:DataGrid.Columns>
                <sdk:DataGridTemplateColumn Width="35">
                    <sdk:DataGridTemplateColumn.CellTemplate>
                        <DataTemplate>
                            <Canvas >
                                <Button x:Name="Rmv1" Background="{Binding Name, Converter={StaticResource converter}}" Width="30" Content="X" VerticalAlignment="Center" HorizontalAlignment="Center"></Button>
                            </Canvas>
                        </DataTemplate>
                    </sdk:DataGridTemplateColumn.CellTemplate>
                </sdk:DataGridTemplateColumn>
                <sdk:DataGridTextColumn Header="Name"  Binding="{Binding Name}"/>
                <sdk:DataGridTextColumn Header="id" Binding="{Binding id}"/>
               
            </sdk:DataGrid.Columns>
        </sdk:DataGrid>
    </Grid>