So, Kazakhstan means 'land of the Kazakhs, Tajikistan is 'land of the Tajiks', and so on.
The not-so-simple explanation
When thinking about how languages evolved, it's easiest to imagine a tree. One of these trees is called 'Indo-European', which branches out in eight directions, including Germanic, Italic, Helenic and Inod-Iranian.
Like any good tree, these branches subdivide out into dozens of languages. For example, follow a Germanic language like Saxon, and you eventually reach English.
Follow Indo-Iranian to Iranian and you'll find Persian. You'll also find Hindi-Urdu and Pashto, which are the respective official languages of Pakistan and Afghanistan.
Across the entire Indo-European tree, the root '-sta' means 'to stand', meaning the Seven Stans are the only countries but not the only places with this suffix.
In Russia, -stan means "settlement", and you can find republics like Dagestan and Tatarstan.
Northwest China has Uyghuristan, Turkey has Elbistan while Iraq has Kurdistan.
Despite sharing suffixes, the seven stan countries weren't all named at the same time.
Pakistan was named less than a century ago. In 1930, the country was named an acronym of its constituent cultures: Punjabi, Afghani, Kashmiri, Sindhi and Balochistan. An additional 'I' was added to help pronunciation.
Language isn't fixed; words and their meanings are constantly being renegotiated and repurposed.
For younger generations, the word 'stan' won't elicit thoughts of Asian nations or places but an obsessive celebrity fan.
A portmanteau of 'fan' and 'stalker', the word alludes to the 2000 song 'Stan' by rapper Eminem, and reached peak zeitgeist in 2019. Merriam-Webster entered it into their dictionary the same year as both a noun and verb.