Assign ICEWS events to administrative regions from GDAM data

I am trying to assign violent events in Afghanistan which are recorded in the ICEWS data (alongside their latitude and longitude) to the relevant districts as recorded in the Global Administrative Area Database (GDAM) using R. This is the first time that I am dealing with geospatial data and am not sure what is the common/efficient approach to do so. My aim is to create based on the assignment of event to a district a new variable in the former dataset with the district’s name.

From sorting through answers to related questions it seems that assigning points to polygons or spatial join may be relevant, and that the SF or GDMAtools packages may come handy.

However, I could not find a directly comparable question and answer.