"An Historical Atlas of Central Asia" written by Yuri Bregel. This is stated on Page no 71 of this book.

The name Uzbek as an ethnic marker appeared sometime in the 14th century (see map 20).There is disagreement among scholars as to the origin of this name, but the old traditional view still seems to be preferable; according to it, this name goes back to the name of Uzbek Khan, the ruler of the Golden Horde in 1313-1341, who was credited with the conversion of his nomadic subjects to Islam. During the conquest of the sedentary regions of Western Turkestan by Shïbani Khan and then the conquest of Khorezm by the #Arabshahid sultans in the early 16th century (see map 25), a substantial number of the tribal groups of the Özbek Ulus migrated to these regions, and it was these tribes that later were known as Özbeks, as distinct from the nomads who remained in the Dasht-i Qïpchaq and were called Qazaqs.
According to a theory widely accepted by Soviet scholars in the 1940s and still current among modern scholars in Uzbekistan, the Turkic speaking tribes of the Dasht-i Qïpchaq who came to Mavarannahr were gradually absorbed by the local Turkic-speaking population, while the latter adopted the name Uzbek “as the last component” of their ethnic identity. In fact, however, the old Turkic-speaking (and even much less so the Tajik-speaking) population of the sedentary regions, as a rule, did not absorb the nomadic newcomers so easily. Until the revolution of 1917 in Russia, the name Özbek was applied in Central Asia only to the tribal population. The Turkic-speaking sedentary population, which had been formed for many centuries through the process of the Turkification of the indigenous Iranians (Tajiks), was called by others and by themselves Sart in Khorezm, Tashkent, and Ferghana (where this population formed a majority by the 16th century) and Chagatai (or Chighatoy) in Mavarannahr.
It was only after the “national delimitation of Central Asia” (see map 46), which was followed by an aggressive policy of “Özbekization” of the population of Uzbekistan, that all the Turkic-speaking (and very often also Tajik-speaking) population of this republic became officially “Uzbeks.”

After the conquest of the sedentary regions of Central Asia by Shïbani Khan, the Uzbek tribes gradually occupied many parts of the irrigated regions until then inhabited by the Tajiks, Starts, and Chagatai's; in Mavarannahr they often replaced these earlier inhabitants and pushed them back eastward, to the mountainous areas; in the mountainous regions themselves, the Uzbeks would usually occupy the lower parts of the river valleys. Central Asian sources give two different lists of Uzbek tribes, one containing 32 names and another 92 names. The origin of these lists, which were wide-spread in Central Asia, is not known, and quite a few of these names (especially in the long list) are found not among the Uzbeks, but among other Turkic, and even non-Turkic, peoples. But the actual number of Uzbeks tribes was indeed somewhere around 30.