Etymology

The name Afghānistān translates to the "Land of Afghans". Its modern usage derives from the word Afghan.

Origin of the word "Afghan"
There are different theories about the origin of the word Afghan, its age, and its meaning. Some believe that "Afghan" is formed from "Apagân". The Pashtuns began using the term Afghan as a name for themselves from at least the Islamic period and onwards. According to W. K. Frazier Tyler, M. C. Gillet and several other scholars, "The word Afghan first appears in history in the Hudud-al-Alam in 982 AD."
In this regard the Encyclopædia Iranica states:
From a more limited, ethnological point of view, "Afghān" is the term by which the Persian-speakers of Afghanistan (and the non-Paštō-speaking ethnic groups generally) designate the Paštūn. The equation [of] Afghan [and] Paštūn has been propagated all the more, both in and beyond Afghanistan, because the Paštūn tribal confederation is by far the most important in the country, numerically and politically.
It further explains:
The term "Afghān" has probably designated the Paštūn since ancient times. Under the form Avagānā, this ethnic group is first mentioned by the Indian astronomer Varāha Mihira in the beginning of the 6th century CE in his Brihat-samhita.

Meaning and origin of the name "Afghanistan"
The last part of the name, -stān, is an Iranian suffix for "place", prominent in many languages of the region.
The term "Afghanistan," meaning the "Land of Afghans," was mentioned by the sixteenth century Mughal Emperor Babur in his memoirs, referring to the territories south of Kabul that were inhabited by Pashtuns (called "Afghans" by Babur).
Until the 19th century the name was only used for the traditional lands of the Pashtuns, while the kingdom as a whole was known as the Kingdom of Kabul, as mentioned by the British statesman and historian Mountstuart Elphinstone. Other parts of the country were at certain periods recognized as independent kingdoms, such as the Kingdom of Balkh in the late eighteenth and early nineteenth centuries.
With the expansion and centralization of the country, Afghan authorities adopted and extended the name "Afghanistan" to the entire kingdom, after its English translation, "Afghanland", had already appeared in various treaties between British Raj and Qajarid Persia, referring to the lands that were subject to the Pashtun Barakzai Dynasty of Kabul. "Afghanistan" as the name for the entire kingdom was mentioned in 1857 by Frederick Engels. It became the official name when the country was recognized by the world community in 1919, after regaining its full independence from the British, and was confirmed as such in the nation's 1923 constitution.