I know Afghanistan, Kazakhstan, Kyrgyzstan, Turkmenistan and Uzbekistan respectively are 阿富汗，哈萨克斯坦，吉尔吉斯斯坦，土库曼斯坦，乌兹别克斯坦. But why isn't Afghanistan translated as 阿富汗斯坦 with the 斯坦 suffix for "-stan" like the others?
A summary is that the translation time of "阿富汗" and that of other "斯坦" are not the same. They follow different translation rules.
"斯坦" is just the sound translation of "-stan", which means "the place of". When translating "阿富汗", “斯坦” is missing because the people who translated the name think that it is not necessary to translate it. You will find that the names of countries that were translated very early are all very short.
Other "斯坦" appears later in the 20th century. At that time, the translation is just following the sound so there is "斯坦".
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From my point of view, it's mainly because of 2 reasons:
哈萨克族, 乌兹别克族 and 吉尔吉斯族（usually written as 柯尔克孜族）are included into the 56 official ethnic groups and there are still large groups of people from those origins living in China. So the official need to put "-斯坦" behind those names when referring to the nation itself. But there are no 阿富汗族 somehow in China so it won't be ambiguous when using "阿富汗"
哈萨克, 乌兹别克，吉尔吉斯 and 土库曼 used to be constituent republics of the CCCP(Soviet Union) and was not independent until 1991. But 阿富汗 has always been as an independent nation for years so the translation rules might be different.
阿富汗 (Afghan) is the shortened (and preferred) version of 阿富汗斯坦 (Afghanistan) which is the full transliteration, but no one is using it because Afghanistan was transliterated a long time ago before, 斯坦 was commonly used in the newly formed nations in modern time
We also commonly use 哈萨克, 土库曼, and 乌兹别克 instead of the full transliterations
斯坦-stan just means nation, it can be omitted in Chinese transliteration
The name 阿富汗 is derived from a very similar name "愛烏罕", which exists in Chinese documentation as early as 1759.
Part of north Afghan, called "巴达克山（بد خشان）" was a subject of early Qing dynasty. The country was later conquered by 愛烏罕 (Afghan's Durrani Empire). Those events are documented by the court of Qing.
See the history of Qing (清史稿) for reference.