Label Map
The Label Map task will relabel components that have been moved within or between boards. The Label Map options allow you to play around with the font type, font size, and display units. Options are available for including or excluding part number, component name, or both. The font size ranges from zero to 5 cm. The component labels can contain either a board-specific part number, a part name or both. You can slide the component dimensions, component label or board label size all the way to the left to remove that label type.

Note
This option provide control over the height of these labels and you can turn them off by making the height zero.
If the space between boards is too small to fit the height you specify for board labels it will NOT include the board label.