A lot of nomadic groups in the Central Asia have a name with a "Hun", "Hon", or "Xun" element: Xiongnu, Hu, Huns, Xionites, Hephthalites, Huna, Xwn; Chinese sources also recorded names such as Xunyu, Xianyun, Xianyu, and Xianbei, all begin with a /ɕ/ - although in Old Chinese all these Xs were very likely pronounced as a S; and speaking of S, we also have Saka, Sai, Scythians, and Sarmatians, whose names share a "Sa" or "Si" element. All these groups seemed to have a similar name, shared a similar culture (or two), speak similar languages, but whether they had more common features beyond those elements or not, we don't really know (
@Zaarin might have a lot of things to add with this part).
On the other hand, there is a detail in the Chinese records, which I think I had mention about it in this thread before - according to Chinese sources, many sub-groups and smaller tribes of the nomadic peoples would take the name of a tribe that is the strongest of them as their
common name.
Houhanshu 後漢書 and
Weishu 魏書 explicitly said that, when Xiongnu was defeated by the Eastern Han and moved away, while Xianbei tribes began to move into the steppes, "there were still a great many of Xiongnu tribes remained [on the steppe], they
all began to call themselves 'Xianbei', there fore Xianbei become stronger." Moreover, a lot of Xiongnu surnames with aristocratic origins became Xianbei surnames in the Chinese records during this era.
Basically, although these smaller tribes were ethnically and linguistically different to each other to some extent, but they shared the same "name" and had a common leader, then they became the same "group" in the eyes of the foreign accounts.
Therefore my personal guess is, there was an important tribe/group in the steppes whose name begins with a "Hun" or "Hon", probably a group before the Xiongnu (the earliest name with a /ɕ/ in Chinese records was "Xianyun", about 600-800 years earlier than "Xiongnu"). This tribe was so influential, that a great many nomadic groups loosely related with this tribe began to take this "Hun" name to refer to themselves, and these myriad of groups gradually evolved into Xiongnu, Huns, Xionites, Hunas, etc.