Even more basic google search will tell you it was a gradual adoption by Highlanders to associate with Biblical Ethiopia (Kush)
I never said it wasn’t due to that lol but you claimed it was recent which simply isn’t true.
Also there seems to be early Meroitic influences in pre-Axumite Ethiopia/Eritrea so there reason for claiming Ethiopia may be more complex than simply wanting to identify with Biblical Ethiopia.
Also, on the Ezana stone Ethiopian is equated with Habesha, as in, the Greek portion of the stone says Ethiopia but that term in the Sabean or Ge’ez version is “Habashat”.
“Ezana, son of Ella Amida, king of the Aksumites, the Himyarites, Raeidan, the Ethiopians, the Sabaeans, Silei (Salhen), Tiyamo, the Beja and Kasou, king of kings, son of the unconquered god Ares.”
Notice how Ethiopians are separate from Axumite, they were a specific peoples living in the highlands who ended up being conquered by the Axumites.
I personally think the highlands were made up of a bunch of different people who all fought each other and had differing identities, the most dominant groups ended up taking over and spreading there identity to the rest of the highlands(Axum, Adulis, Agazi and Habesha/Ethiopian)
Agazi for example, are a peoples/polity that are mentioned in the Adulite throne as being subjugated by the king of Adulis, among many other peoples. Tigrinya Eritreans and Tigrayans only recently stopped calling themselves “Agazian”(20th cent) .So that term became an identifier among all Tigrinya speakers who btw are the true inheritors of Axum not the Amhara, this clearly shows certain groups in the highlands in the early Axumite era spread out and conquered the region spreading these identities and replacing the weaker people’s identities.
Basically my point is the highlanders who called themselves Ethiopian were probably a specific tribe/polity that could have had actual Nubian roots, and they simply spread this identity through conquest/assimilation, rather than the entire state adopting the term purely to associate with Biblical Ethiopia.