How to change column header’s background color when using WPF datagrid

Use a style with a setter targeted at DataGridColumnHeader:

<DataGrid>
    <DataGrid.Resources>
        <Style BasedOn="{StaticResource {x:Type DataGridColumnHeader}}" TargetType="{x:Type DataGridColumnHeader}">
            <Setter Property="Background" Value="Blue" />
        </Style>
    </DataGrid.Resources>
</DataGrid>