There are two camps in academia regarding the identity of the huns.

One which claims that the possibility if an east asian nomadic group showing up in Europe with the same name hundreds of years later is unlikely.

This was based solid but dated evidence.

Researcher is Korea are changing this idea as more and more studies are done on nomadic cultures, and nomadic civilization.

Archeology has shown that the Huns where likely a multi racial, multi cultural nomadic confederation of, turkic, mongolic, yenesian, uralic, and iranic peoples who formed a political polity.

Disclaimer* (Nomadic cultural and linguistic identities are fluid and changing that is why you can have populations that are genetically iranic indo european speaking a turkic language)

What likely happened was after the dissolution of the xiong nu state (pronounced hunnu in middle chinese)

The various tribes broke apart while still claiming the hunnic name. They expanded and ended up where they ended up. With attilas ancestors in europe confederating germans tribes the same way the early Xiong nu did in Asia.

This line of research is coming from the perspective that, nomadic peoples are more politically flexible compared to settled agrarians. So we need to shake the bias of looking for one race(kinda why most skeletons show an eurasian mix), culture, language, and archeological evidence.

The xiongnu set the political frame work for other nomadic empires to carve out territories and extract tribute.

This is why chinese records say " these various barbarians are decended from huns". The need to identify ones own tribe as such may have still held political and cultural value.

Hyun Jin Kim: http://asianhistory.oxfordre.com/view/10.1093/acrefore/9780190277727.001.0001/acrefore-9780190277727-e-50

To add to the question: What about the xiongnu? Where they related to the Huns?