Did other cities than Salisbury (now: Harare) change name after the independence of Zimbabwe?

Yes, many of them. Following independence in 1980, Zimbabwe (formerly Rhodesia) began renaming cities, towns and streets, in an attempt to eradicate symbols of British colonialism and white minority rule, starting in 1982, on the second anniversary of independence. The capital Salisbury, which had been named after the British Prime Minister, the 3rd Marquess of Salisbury, was renamed Harare, after the Shona chief Neharawa. Other place names were simply new transliterations, to reflect the correct pronunciation in the Shona language. Hence the city of Gwelo became Gweru. Many places had been denoted with the Ndebele language pronunciation during the colonial period and this generally included the letter "L" which does not exist in Shona.

Complete list here:

https://en.wikipedia.org/wiki/Place_names_in_Zimbabwe