Where are the land of Cush and the land of Havilah today, and what are their names today?
The first mention of Cush is in Genesis 2:13 where the Gihon, one of the four mighty rivers flowing from the land of Eden, encompassed this particular region. Because the great flood of Noah's day wiped out the geography of that time, we have no idea where any of the regions mention in the early chapters of Genesis existed.
After the flood, one of the grandsons of Noah was named Cush. His brothers were Mizraim, Put, and Canaan. All four were founders of nations. Mizraim founded Egypt. Canaan founded the Canaanite city-states in the land of Canaan. Cush founded Ethiopia (just south of Egypt) and Put founded the country we now know as Libya (just west of Egypt). Ethiopia is called the land of Cush, not because it matches the location near Eden, but because its founding ancestor was named Cush.
Havilah was also a region in the pre-flood world that is mentioned in Genesis 2:11. The Pishon flowed around it and it was noted for its gold. After the flood, one of Cush's sons (Noah's great-grandson) was named Havilah. Do you see the trend in this family to name sons after remembered lands from before the flood? Havilah and his descendants settled in the region between the Persian Gulf and the Red Sea, the area we now call the Arabian Desert, on the northwest end.