The names of these algae refer to photosynthesis. In photosynthesis, sunlight is used to produce energy. If you look at the color of the sunlight, you can see that all the colors of the rainbow are included. However, the algae do not absorb all the light, but only certain color components, e.g. everything except the green light. For us, the algae then appear green and are therefore called green algae.
Explanation for children:
Algae need light to perform photosynthesis. Sunlight can be divided into all the rainbow colors and not all algae like the same colors. Depending on which colors they like and use, and which colors they don't like, the algae have different names and different colors.