Why did Zimbabwe only become internationally recognised after a communist revolution?

So I'm going to try and answer this as best I can - Rhodesian/Zimbabwean history is my speciality so if there is anything you want me to go further into detail about, ask away.

First of all, Zimbabwe was not internationally recognised before 1980 because Zimbabwe did not exist before 1980. Southern Rhodesia (or simply Rhodesia from the early 1960s) was the internationally recognised name of the country prior to 1978. In 1978 under the terms of the Internal Settlement and Salisbury Agreement, the nation became Zimbabwe-Rhodesia, and only in 1979 with the Lancaster House agreement, did it become officially renamed as Zimbabwe. Zimbabwe was the name chosen for their independent country by the anti-colonial nationalist forces that struggled against white minority rule in the country for over a decade. Much as any other nation in the world, international recognition depends to a large extent on the nature of the ruling government within the country. During the liberation struggle, and despite the apparent worldwide antagonism to the white Rhodesian Front government of Ian Smith, the country was still legally and technically named Rhodesia.

Now, I just want to highlight something in your question. The liberation struggle in colonial Zimbabwe was not a Communist revolution. As /u/Commustar rightly pointed out, both ZANU and ZAPU (the two principal nationalist groups involved in the struggle) had strong connections to the USSR, China and Cuba in terms of both materials and ideologies. However, this is not to say that either group was a primarily communist movement. The leaders of ZANU and ZAPU (Ndabaningi Sithole/Robert Mugabe and Joshua Nkomo respectively) routinely espoused communist or more specifically, Marxist or Maoist rhetoric but they were first and foremost anti-colonial and pro-majority rule movements whose main aim was the removal of the white minority government in Rhodesia.

If you want, I can provide you with sources tomorrow (when I get back to my books) as to the extent that Marxist ideologies genuinely influenced both the discourse of the liberation struggle and the actions of the nationalist groups during that period. Some academic work has already been done on just this topic of communism and the Zimbabwean liberation war, and the overarching conclusion is that context is key. Mugabe and Nkomo made public declarations of Marxist ideologies because they saw it as their best chance of getting the supplies they needed to wage a large-scale guerilla war against a well-armed and well-stocked white state. Due to the nature of the Cold War on a global scale, and despite the legitimate disdain the US and the West had against the continuation of white minority rule in Rhodesia, the West was even more fearful that majority rule in the nation would open the door to a communist insurgency throughout the African continent. Consequently, Nkomo and Mugabe were almost entirely dependent on Soviet or Chinese support as they were largely ignored by Western and American governments.

Perhaps this isn't the issue I have made it out to be, but describing the liberation struggle in colonial Zimbabwe as a "communist revolution" does a disservice to the hundreds of thousands of black Zimbabweans who fought not for ideological reasons but for their own independence from white minority rule and British colonialism and a system that classified them as second-class citizens in their own country. As a final remark on the extent to which it could be called a "communist revolution", I would highlight what happened after independence in 1980, when Robert Mugabe and his ZANU-PF party were elected into power. Despite a manifesto claiming socialist goals and agendas, the nation remained almost entirely capitalist in nature. Some minor changes, such as the introduction of a Politburo in government and state purchase of land, nevertheless remained ingrained in a staunchly capitalist society, both economically and politically.

Any further questions, please fire away. I'm sorry I haven't referenced specific texts here, but I will promise to do so as soon as I can tomorrow morning.