Yup the Country of Ghana is named after the Kingdom of Ghana and the Country of Mali is named after the Kingdom of Mali. It has to also be mentioned that when Ghana is mentioned then the Ivory Coast has to also be mentioned.
Right on the website of Ancestry.com they explain of the history of Ivory Coast and Ghana:
Ivory Coast/Ghana
Primarily located in: Ivory Coast, Ghana
Also found in: Benin, Togo, Mali, Nigeria, Senegal
Early French and Portuguese explorers identified sections of the West African coast by the area’s resources, which is how Côte d'Ivoire, or Ivory Coast, got its name.
Neighboring Ghana was known as the Gold Coast until it won independence from colonial rule in 1957 and renamed itself after a medieval West African empire. Today, more than 46 million people live in the two countries, which depend less on gold and ivory than they do chocolate: Ivory Coast and Ghana produce more than half of the world’s cocoa.
There is evidence of human activity in the area of modern-day Ivory Coast and Ghana going back millennia. Some groups, such as the Akan, trace their history in the region to at least the 11th century. Historians believe that most current populations were in place by the 16th century after absorbing or displacing previous inhabitants. Ghana and Ivory Coast are each home to more than 60 different ethnic groups today.
Geography played an influential role on the populations of Ghana and Ivory Coast. In both countries, the terrain ranges from savanna in the north to forest in the south. The dense forests acted as partial barriers to trade, migration and forming large, centralized societies like those that appeared farther north, where vast empires rose and fell for more than a millennium. The north-south divide is also evident in religion: Islam came to West Africa with the trans-Saharan trade and is more prevalent in the north; Christianity, introduced by Europeans, gained a foothold in the south.
A woman walks through dense forests in central Ghana
Migrations into Ivory Coast and Ghana
Modern Ivory Coast and Ghana lie on the periphery of the great empires of Mali (ca. 1230–1550) and Songhai (ca. 1375–1591), and the region’s population felt their influence. As empires rose and fell, people pushed into new lands or fled old ones. Dyula (or Juula) traders, a merchant class of Mandé people from Mali, made their way south, introducing goods, inhabitants and Islam to the northern edges of modern-day Ghana. They later established the Kong Empire (1710–1898) in northeastern Ivory Coast. Other Mandé groups settled in western Ivory Coast, where they make up almost 25% of the population today.
According to their own oral tradition, the Dagomba people came from the area northeast of Lake Chad, finally settling in northern Ghana. The Senufo came south from Mali into Ivory Coast in about the 15th century. The Ewe people migrated from the east, from the areas now making up Togo and Benin.
The most significant migration for Ghana and Ivory Coast, however, began with the arrival of the Akan people. The Akan had established the state of Bonoman—a center of trade for gold, salt, kola nuts, ivory and leather—in western Ghana/eastern Ivory Coast. From Bonoman, they spread out looking for gold.
The Akan people
With a population of 20 million, the Akan represent the largest ethnic group in Ghana and Ivory Coast. The Akan are a matrilineal society believed to have originated in the Sahel region and who then traveled south into Ghana and Ivory Coast.
The Ashanti, a subgroup of the Akan, formed a number of states in Ghana built around trade and gold. They traded with the Songhai and Hausa along traditional inland routes and also with European partners, starting with the Portuguese, who arrived on the coast in 1482. New crops, such as maize and cassava, and slave labor allowed them to push farther into the forests, clearing land to farm and mining gold. In fact, before the transatlantic slave trade began in earnest, the Ashanti bought slaves from the Portuguese.
The Ashanti Empire was established in 1701 by Osei Tutu, who began unifying Ashanti states around the city of Kumasi. The Ashanti continued to expand, through diplomacy and military conquest, building one of the most advanced and powerful empires in sub-Saharan Africa. Not all Akan people wanted part in the empire, and some fled west into modern-day Ivory Coast. These included the Abron, the Baoulé and the Agni. In the 19th century, the Ashanti fought a series of wars with British troops, as England tried to firm up its hold over Ghana. Eventually, the Ashanti kingdom, known as Asanteman, became a British protectorate in 1902 and today is a state within modern Ghana.
Defeat of the Ashantis by British forces, July 11, 1824
French sovereignty over Ivory Coast was recognized by the British in 1889, and the country became a French colony in 1893. Ivory Coast continued to attract new immigrants in the 20th century when two decades of prosperity and relative peace followed independence in 1960.
Please note that genetic ethnicity estimates are based on individuals living in this region today. While a prediction of genetic ethnicity from this region suggests a connection to the groups occupying this location, it is not conclusive evidence of membership to any particular tribe or ethnic group.
Did You Know?
The Ashanti had their own telegraph long before American inventor Samuel Morse patented his (in 1847). The Ashanti people sent messages through the forest via drum. The tones of their famous “talking drums” mimic their own tonal language.
Ashanti drummer with talking drums