This is more of a linguistic question than a historical one. Despite your claim that "Iran" إراب Ērān does not have -stan in its name, it actually does but in a different form! In Modern Persian, ـستان‏ -estan means home of, or a place of. So Pakistan would be the home of Pakis or rather land of the Pure, پاک‏ Pak which means pure and holy. Iran used to be called in Middle Persian ایرانشهر‏ Ērānšahr, شهر sahr which is an obsolete word for land, country, kingdom and ایران‏ Ērān where -ān denotes the plural of ēr- which means "of the Iranians". ایران‏ Ērān simply became the abbreviated form of ایرانشهر‏ Ērānšahr where ایرانشهر‏ Ērānšahr means "Kingdom (ruled by) Iranians" from the Sassanian Dynasty in the 3rd century C.E. And ایران‏ Ērān abbreviated to "Land of the Iranians". The Roman west corresponded by naming the area “anērān". Šāpūr I, the second shahanshah (kings of kings) of the Sassanian empire in the 3rd century C.E. used this shorten form of ایران‏ Ērān when naming several towns he and his successors founded, such as Ērān-xwarrah-Šābuhr “The glory of Ērān (of) Šāpūr,” Ērān-āsān-kard-Kawād “Kawād pacified Ērān."

Source:

Gnoli, Gherardo. The Idea of Iran: An Essay on Its Origin. Roma. 1989.

MacKenzie, D. M. Kerdīr’s inscription. in ed. G. Herrmann, The Sasanian Rock Reliefs at Naqsh-i Rustam, Iranische Denkmäler 13. Berlin. 1989.

EDIT: Persian and English characters don't like each other :(