Do we know what they called themselves? Hittites is a name used in the Bible and later historians gave that name to this people. I know their language was called nesili (Neshite) but I can't seem find a source where their native name for themselves is mentioned.
Thanks!
That is, in fact, because they did not name themselves like a distinct ethnic group (which makes sense, since they never were a homogenous ethnic group).
Instead, they called themselves "men/sons of the land of Ḫatti", or, written LU.MES URU ha-at-ti. (Please note that out ot formatting reasons, I did not use special signs)
There are some variations like LU.MES URU ha-at-ti-KI, which is probably based on old hittite URU ha-at-tu-su-um-ma, implying "people of (the city) of Hattusha", but a word like "Hittites" does not exist until the end of the 2. millenium BC.
Source: J.Friedrich e.a., Altkleinasiatische Sprachen (Und Elamitisch), in: HbO 2, Keilschriftforschung und Alte Geschichte Vorderasiens, Leiden/Köln, 1969, S. 125-126
The term "Hittite" does come from the biblical "Heth," but that itself is a derivation from the term "Hatti" which was apparently used to refer to the land around Hattusa, an important Hittite city in Central Anatolian. The Hittite Empire encompassed multiple languages across time and space, and the form "Hatti" seems to have been derived from the language (Hattic, an non-indo-european agglutinative isolate) spoken in the area before the nešili speakers came to prominence. I'm afraid I don't know of any other autonyms for the peoples of the geopolitical abstraction known as the Hittite Empire, but it's a safe bet that there were several in use.