As is often the case when the names of African countries appear to suddenly change names, the answer is that the end of the colonial era caused a change in the identity of the people in power in the country, and the people newly in power changed the name.

But you probably want some more detail.

The area of modern Zimbabwe was controlled by the British from roughly the 1880s through the 1960s. They named the territory after Cecil Rhodes, a British businessman who played an influential role in the development of British interests in southeast Africa.

When the British decolonized most of their African colonies, they were unable to decolonize Rhodesia. The problem was that British policy required, as a prerequisite to decolonization, that colonies must have adopted policies of majority rule prior to the decolonization. The British-ancestry settlers of Rhodesia resisted this, and ended up declaring independence without approval from Britain, setting up a South Africa-style whites-only government.

The result was a decade and a half of civil war between the (unrecognized) Rhodesian government and (disenfranchised) black activists, complicated by the fact that Rhodesia's government simultaneously claimed to be loyal to the Queen and refused loyalty to her appointed colonial representative.

The situation continued until 1979, when the involved parties negotiated a truce and a plan for a transition to majority rule government.

The incoming majority rule government had no great love for the name 'Rhodesia', which had become a symbol of the oppressive white supremacist state, and reached back into their history for a new name: Zimbabwe, the name of a great iron age African kingdom (whose territory overlapped the modern Zimbabwe. This represented the abandonment of a hated colonial name and a public restoration of the past, and it was an attempt to symbolically suggest that the new Zimbabwe would be as great as the old Zimbabwe had been.