PP3 decides which labels are printed on the map by itself. But, of course, you can configure this behaviour, and you can delete or add any label.
For example, the command
delete_labels NGC 884 NGC 869 TAU 27 ;
deletes the labels for the nebulae NGC884 and NGC869, and for the star 27Tau from the map. The nebulae and the star themselves remain on it of course. Correspondingly,
add_labels CNC 65 CNC 47 CNC 43 CNC 48 ;
adds the currently set labels texts for the stars 65, 47, 43, and 48Cnc. All of them are too faint to get their labels implicitly.
But you can also influence labels globally in the parameters section of the input script. If you don't want to have any labels at all, simply say
switch labels off
in the parameters section. Another parameter keyword is
set faintest_star_with_label_magnitude 2.0
which means that only stars of brightness of at least 2.0m get an implicit (automatic) label.