How do I make a header for a ListBoxItem?

WPF provides some properties just for this purpose. You need to use the SharedSizeGroup and Grid.IsSharedSizeScope properties:

<Grid Grid.IsSharedSizeScope="True"><!-- Look HERE -->
    <Grid.RowDefinitions>
        <RowDefinition Height="1*" />
        <RowDefinition Height="7*" />
    </Grid.RowDefinitions>
    <!--  Title  -->
    <Grid>
        <Grid.ColumnDefinitions>
            <ColumnDefinition SharedSizeGroup="FirstNameColumn" /><!-- Look HERE -->
            <ColumnDefinition />
        </Grid.ColumnDefinitions>
        <Border Style="{StaticResource borderBase}">
            <TextBlock Text="FirstName" />
        </Border>
        <Border Grid.Column="1" Style="{StaticResource borderBase}">
            <TextBlock Text="SecondName" />
        </Border>
    </Grid>
    <!-- Data -->
    <ListBox Grid.Row="1">
        <ListBox.ItemTemplate>
            <DataTemplate>
                <Grid>
                    <Grid.ColumnDefinitions>
                        <ColumnDefinition SharedSizeGroup="FirstNameColumn" />
                        <ColumnDefinition /><!--  Look Above HERE  -->
                    </Grid.ColumnDefinitions>
                    <Border Style="{StaticResource borderBase}">
                        <TextBlock Style="{StaticResource textBlockBase}" Text="{Binding FirstName}" />
                    </Border>
                    <Border Grid.Column="1" Style="{StaticResource borderRigth}">
                        <TextBlock Style="{StaticResource textBlockBase}" Text="{Binding SecondName}" />
                    </Border>
                </Grid>
            </DataTemplate>
        </ListBox.ItemTemplate>
    </ListBox>

</Grid>

Please se the Grid.IsSharedSizeScope Attached Property page at MSDN for more information.

Why so complicated? Just use the GridViewColumn's "Header" attribute...

 <ListView >
            <ListView.View>
                <GridView>
                    <GridViewColumn  Header="Id"/>
                    <GridViewColumn  Header="Name"/>
                </GridView>
            </ListView.View>
        </ListView>

I would recommend using a ListView, there you can define and style headers for each column and don't have to care about the positioning:

    <ListView>
        <ListView.View>
            <GridView>
                <GridViewColumn>
                    <GridViewColumn.CellTemplate>
                         <Border Style="{StaticResource borderBase}">
                             <TextBlock Style="{StaticResource textBlockBase}" Text="{Binding FirstName}" />
                         </Border>
                    </GridViewColumn.CellTemplate>
                    <GridViewColumn.HeaderTemplate>
                        <!--your header template-->
                    </GridViewColumn.HeaderTemplate>
                </GridViewColumn>
                <GridViewColumn>
                    <GridViewColumn.CellTemplate>
                         <Border Style="{StaticResource borderBase}">
                             <TextBlock Style="{StaticResource textBlockBase}" Text="{Binding SecondName}" />
                         </Border>
                    </GridViewColumn.CellTemplate>
                    <GridViewColumn.HeaderTemplate>
                        <!--your header template-->
                    </GridViewColumn.HeaderTemplate>
                </GridViewColumn>
            </GridView>
        </ListView.View>
    </ListView>