The stacked chart doesn't currently listen for the keys and auto generate the series again. The best thing for you to do would be to put the GroupBy in your view model, and change the group by when the data source changes as well.
Here is an example:

<UserControl.Resources>
        <local:KeyConverter x:Key="keyConverter" />
        
        <DataTemplate x:Key="keyLegendItemTemplate">
            <StackPanel Orientation="Horizontal" Margin="1" Visibility="{Binding Series.Visibility}">
                <ContentPresenter Content="{Binding}" ContentTemplate="{Binding Series.LegendItemBadgeTemplate}" />
                <ContentPresenter Content="{Binding Series.ValueMemberPath, Converter={StaticResource keyConverter}, ConverterParameter='_Emission'}"/>
            </StackPanel>
        </DataTemplate>
    </UserControl.Resources>

    <Grid x:Name="LayoutRoot" Background="White">
        <Grid.ColumnDefinitions>
            <ColumnDefinition />
            <ColumnDefinition Width="Auto" />
        </Grid.ColumnDefinitions>
        <Grid.RowDefinitions>
            <RowDefinition/>
            <RowDefinition Height="Auto" />
        </Grid.RowDefinitions>
        <igChart:XamDataChart x:Name="theChart"
                              Legend="{Binding ElementName=legend1}">
            <igChart:XamDataChart.Axes>
                <igChart:CategoryXAxis x:Name="xAxis" 
                                       ItemsSource="{Binding Data}"
                                       Label="{}{Key}"/>
                <igChart:NumericYAxis x:Name="yAxis" />
            </igChart:XamDataChart.Axes>

            <igChart:XamDataChart.Series>
                <igChart:StackedColumnSeries x:Name="stack"
                                             ItemsSource="{Binding Data}"
                                             XAxis="{Binding ElementName=xAxis}"
                                             YAxis="{Binding ElementName=yAxis}"
                                             AutoGenerateSeries="True"
                                             LegendItemTemplate="{StaticResource keyLegendItemTemplate}"
                                             >
                   
                </igChart:StackedColumnSeries>
            </igChart:XamDataChart.Series>
        </igChart:XamDataChart>
        
        <igChart:Legend x:Name="legend1" Grid.Column="1" />
        
        <Button Grid.Row="1" x:Name="changeData" Content="Change Data" Click="changeData_Click" />
    </Grid>
</UserControl>

and code behind:

public partial class MainPage : UserControl, INotifyPropertyChanged
    {
        public MainPage()
        {
            InitializeComponent();

            Data = new GroupBy()
                {
                    ItemsSource = GetValuesOfExcessVsEmissionsEnterprise(2000),
                    GroupMemberPath = "Date",
                    KeyMemberPath = "Name",
                    ValueMemberPath = "Emission"
                };

            DataContext = this;
        }

        private GroupBy _data;
        public GroupBy Data
        {
            get
            {
                return _data;
            }
            set
            {
                _data = value;
                if (PropertyChanged != null)
                {
                    PropertyChanged(
                        this,
                        new PropertyChangedEventArgs(
                            "Data"));
                }
            }
        }

        public List<ExcessVsEmissions> GetValuesOfExcessVsEmissionsEnterprise(int year)
        {
            var TestEmissionsCollection = new List<ExcessVsEmissions>();

            for (int i = 1; i <= 12; i++)
            {
                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 4500,
                    Date =
                        (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 4000,
                    Id = new Guid(),
                    Name = "Enterprise 1",
                    ParentId = null,
                });
                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 3500,
                    Date =
                        (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 2000,
                    Id = new Guid(),
                    Name = "Enterprise 2",
                    ParentId = null,
                });
                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 2000,
                    Date =
                        (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 1800,
                    Id = new Guid(),
                    Name = "Enterprise 3",
                    ParentId = null,
                });

                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 10000,
                    Date = (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 10000 - 7800,
                    Id = null,
                    Name = "Emisiones Totales",
                    ParentId = null,
                });
            }

            return TestEmissionsCollection;
        }

        public List<ExcessVsEmissions> GetValuesOfExcessVsEmissionsInstallation(int year)
        {
            var TestEmissionsCollection = new List<ExcessVsEmissions>();

            for (int i = 1; i <= 12; i++)
            {
                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 500,
                    Date =
                        (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 400,
                    Id = new Guid(),
                    Name = "Instalacion 1",
                    ParentId = null,
                });
                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 1000,
                    Date =
                        (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 1100,
                    Id = new Guid(),
                    Name = "Instalacion 2",
                    ParentId = null,
                });
                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 2000,
                    Date =
                        (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 500,
                    Id = new Guid(),
                    Name = "Instalacion 3",
                    ParentId = null,
                });
                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 3000,
                    Date =
                        (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 2800,
                    Id = new Guid(),
                    Name = "Instalacion 4",
                    ParentId = null,
                });
                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 4000,
                    Date =
                        (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 3000,
                    Id = new Guid(),
                    Name = "Instalacion 5",
                    ParentId = null,
                });
                TestEmissionsCollection.Add(new ExcessVsEmissions()
                {
                    Assignation = 10000,
                    Date =
                        (i.ToString() + " / " + year.ToString()[2] + year.ToString()[3]),
                    Emission = 10000 - 7800,
                    Id = null,
                    Name = "Emisiones Totales",
                    ParentId = null,
                });
            }

            return (TestEmissionsCollection);
        }

        public event PropertyChangedEventHandler PropertyChanged;

        private void changeData_Click(object sender, RoutedEventArgs e)
        {
            Data = new GroupBy()
            {
                ItemsSource = GetValuesOfExcessVsEmissionsInstallation(2000),
                GroupMemberPath = "Date",
                KeyMemberPath = "Name",
                ValueMemberPath = "Emission"
            };
        }
    }

    public class ExcessVsEmissions
    {
        private Guid? _parentId;

        public Guid? ParentId
        {
            get { return _parentId; }
            set
            {
                _parentId = value;
            }
        }

        private Guid? _id;

        public Guid? Id
        {
            get { return _id; }
            set { _id = value; }
        }

        private string _name;

        public string Name
        {
            get { return _name; }
            set
            {
                _name = value;
            }
        }

        private Decimal? _emission;

        public Decimal? Emission
        {
            get { return _emission; }
            set
            {
                _emission = value;
            }
        }

        private string _date;

        public string Date
        {
            get { return _date; }
            set
            {
                _date = value;
            }
        }
        private Decimal? _assignation;

        public Decimal? Assignation
        {
            get { return _assignation; }
            set { _assignation = value; }
        }
    }

    public class KeyConverter
        : IValueConverter
    {

        public object Convert(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
        {
            if (value is string && parameter is string)
            {
                var key = (string)value;
                var param = (string)parameter;

                key = key.Replace(param, "");

                return key;
            }

            return "";
        }

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

Hope this helps!
-Graham

It works now, thank you very much!!

I will hit now for the legend that is not really working and I will try to put a tooltip foreach stacked item