The small hole in pen caps serves four main purposes

Safety: Reduces choking risks by allowing air to pass through if the cap is swallowed, lowering the chance of suffocation. This feature is especially important for children who tend to put objects in their mouths.
Smooth Writing: Acts as a pressure vent, preventing air buildup that can cause leaks or inconsistent ink flow due to changes in temperature or altitude.
Cost and Manufacturing: Less plastic is needed, and the molding process becomes easier, resulting in significant savings when producing millions of pens.
Design Element: Some companies use the hole to enhance aesthetics or branding, incorporating it into their visual identity.
The International Organization for Standardization (ISO) requires pen caps to have a hole that allows a minimum airflow of 8 liters per minute to reduce the risk of asphyxiation if swallowed. This standard applies to writing instruments likely to be used by children under 14.