There are 3 network operators in the country:

There are many small reseller offices in airports, train stations and shops, but their employees mostly don't speak English (except possibly in airports). You are required by law to present your ID (or passport) at the point of purchase. This used to be enforced not so strictly in the past, but from 2018 registration is much stricter now.

From 1st January 2019 all devices using local Kazakh mobile SIM cards must be registered (with a few exceptions, like M2M devices and foreign devices roaming in Kazakhstan).The registration is done automatically, nationals need to bind their national ID number "ИИН" (IIN) to their mobile account. Foreigners need to submit their passport number.

It works the following way: If it's the first time that device connects to the network, its IMEI number and personal identification number that were associated to the mobile account will be submitted to a common government database (called BDIK) to link it together. After that, the device is locked-in to that person's personal data and cannot be used with any other SIM card from a Kazakh operator that is not registered to the same "IIN" or other personal ID number (with the exception of foreign SIM cards).