I don't know the etymological meaning of Wawat. The etymology of kushite: ḫ_s, is determined by geography and ethnicity. The vowel associated with K_sh can be an /a/,/e/ or /u/. The root word is interpreted as a geographical term probably meaning hilly area.
The surrounding non Kush populations usually refered to the people living in these hilly areas as "blacks" or Nehesy. Thusly, Kush would mean "hilly land where the Nehesy [from the Sudan] live. I have not been able to determine what the etymology of Kush is based on the Kushite languages up to now.
The Kushites were originally called ḫЗšt ,Ta-Seti, Nehesy and Tehenu by the Egyptians The Kushites were called ḫ3s.t(j) beginning in Narmer’s time, and k3š in Middle Egyptian beginning with the 18th Dynasty.
The Kushites were called ḫЗst from Nubia and Taleh (Lower Egypt) into the Levant. Kushites had early settled in the Levant since Narmer times. We find Narmer's name on jars and serekhs from excavations in Israel and Palestine , for example Tel Erani, Arad, 'En Besor, Halif Terrace/Nahal Tillah and more(4). A bulla dating to this period makes it clear that this part of the Negev was called ḫЗts.t ("Kush") or ḫ3s.tj ("Kushite").
The Old Kingdom rulers also referred to the Kusites in Nubia as ḫ3st .
Most researchers accept the contemporary meaning of Gardiner's N25 symbol as "Rulers of foreign lands" not Kush”. But this was not the first meaning assigned this sign. Breasted translated N25, as "heqa ḫ3st ". In my book the Kushites, Who, What, When, Where, I explain that the Hyksos were Blacks native to Lower Egypt.
Semantically reading N25 as "Rulers of foreign land" is unintelligent, for example “Wawat Rulers of foreign lands” , is incorrect, because Wawat was the name of a nation, not a king. As a result, ḫ3st, was used to identify the nationality of the Wawat, Kau and other Kushite = ḫ3st.
Thusly, the inscription of Weni line 46 : “His majesty made war on the Asiatic Sand-dwellers and his majesty made an army of many ten thousands; in the entire South, southward to Elephantine, and northward to Aphroditopolis [Busiris]; in the Northland on both sides entire in the [stronghold], and in the midst of the [strongholds], among the Irthet "heqa ḫ3st [Kusites], the Mazoi "heqa ḫ3st [Kushites], the Yam "heqa ḫ3st [Kushites], among the Wawat "heqa ḫ3st [Kushites], among the Kau "heqa ḫ3st [Kushites], and in the land of Temeh.”
The Hyksos were also referred to as ḫ3st. The Hyksos ruled from 1650-1550.
The New Kingdom lasted from 1549-1292. During the New Kingdom Egyptians used the name Aamw, as a generic name for the Asian, the term : Habiru, was ethnonym for one of the Asian tribes. It is clear that if the Habiru and Heqa Khasut were the same people, they would have had the same name given the fact the New Kingdom, began at the end of the Heqa Khasut Dynasty.
There are many Hyksos inscription where they were identified as ḫ3st . The Hyksos door jamb signs reads “King of the Kushites. ḫ3st is also found on the Hyksos scarabs. These scarabs often begin with the title Heqa ḫ3st and the plural marker III, and should read “King of the Kushites”.
This is obvious when we look at the Khnumhotep II, inscription. Here we see above a Nubian ibis heqa ḫЗst, under the ibis is the name Abisharie. This inscription reads: "The Kushite King Abisharie".
The Greeks called Kush: Ethiopia.
The earliest mention of the term k3š , is mentioned on the Buhen stela from the Sety1 (1294-1279). Kush was also written “KSH” in Egyptian text dating between 1550-1069 BC.
The native name of the Kingdom was recorded in Egyptian as k3š, based on the New Kingdom-era Akkadian transliteration as the genitive kūsi.
It is also an ethnic term for the native population who initiated the kingdom of Kush. The term is also displayed in the names of Kushite persons, such as King Kashta (a transcription of k3š-t3 "(one from) the land of Kush"). Geographically, Kush referred to the region south of the first cataract in general. Kush also was the home of the rulers of the 25th dynasty.
Some researchers believe Kush was derived from Qvs. Kush can not be derived from Qevs, there is no 'v', in Meroitic.
The Meroites called themselves Qus, but we may never know the exact meaning of Kush. L. Torok and J. Leclant have found In the Meroitic text that the Meroites referred to themselves as Qeš. I noted that in the Tanyidamani Stelas the Meroites called themselves Kushites/Qoshites. In the Tanyidamani inscription we read Qor ene Tañyidamani ne al e Qosne I bl p mni , “The Monarch, the Commander, the good and noble Tañyidamani, give [this] Kushite leave to praise and to supplicate Amani”.
The Handbook of Oriental Studies (New York:Brill,1997) out lines the history of the term Kush in relation to the Kushites on pages 2-3. Torok points out that the name for the first ruler of the Twenty-Fifth Dynasty, Kashta, probably meant "the Kushite" his nomen was k3š-t3 "of the land of Kush". He also noted that Kush, also appears as the ancestral kingdom of Piya in his Sandstone Stela and King Arqamani in the Second Century BC received the mortuary Horus name "The Kushite whose-coming-into-being -is divine".
The textual evidence make it obvious that the people of Meroe, and earlier rulers of Kerma and Napata from the same region, may have called themselves Kushites.
The people of Upper Nubia and the Sudan were known in Egyptian as k-'-s and k-'-s-I, as ḫЗts.t or Khasut which corresponds to Kashit and k3š-t3. The Hebrew people called the Kushites kus. In the cuneiform inscriptions the Sudanese were called Kusiya. In the Ethiopic inscriptions of Ezana, the Kushites were called Kashi or Kasu. In Sumerian the Kushites were called Melukha = Kasi and Kasi = Kush. The Meroites identified themselves as Qoš, Qes, Qos.
In conclusion, the presence ḫ3st in Line 46 of the Weni Inscription and the Narmer bulla indicates that since this area was called ḫЗts.t or Kush, since Narmer ruled the area he was a Kushite.
The k3š seems to have been used to refer to the Kushites during the New Kingdom.
The modern interpretation of Gardiner’s Egyptian sign N25 as ḫЗts.t is wrong. There is no evidence that /t/ should be added to ḫЗts.t, as a result I believe N25 was originally ḫЗs, not ḫЗst . Writing just Heqa ḫЗst means Kushite King, while adding three lines makes the plural: King of the Kushites.
Thusly on the Semqen scarab we have Semqen king of the Kushites. On the Khnumhotep II Beni Hassan inscription we have Heqa ḫЗst in front of the lead Hyksos above the Nubian ibis, and the name Abisharie below heqa ḫЗst.