ArcReader does not allow you to change the visibility of labels within the published map document. A scale range for the labels can be set within ArcMap before the .pmf file is published, which can provide some relief if the map is crowded with labels.
Viewing labels
ArcGIS Desktop is in mature support and will be retired March 1, 2026. There are no plans for future releases of ArcGIS Desktop, and it is recommended that you migrate to ArcGIS Pro. See Migrate from ArcMap to ArcGIS Pro for more information.