A map uses different shades of colour to show the population density in different regions of a country.
What is the name of this type of map?

A choropleth map is a type of thematic map in which areas are shaded or patterned in proportion to the measurement of the statistical variable being displayed on the map, such as population density or per-capita income. The map described, showing population density by shading different regions, is a classic example of a choropleth map.