It is a reference to the Biblical account of the dying Rachel giving birth to Benjamin, whom she named Ben-Oni.

[1] In 1825 Aaron Reinganum, a prominent member of the Frankfurt Jewish community, published a book entitled Ben-Oni oder die Vertheidigungen gegen die Gambitzüge im Schache in which he analyzed several defenses to the King's Gambit and the Queen's Gambit, as well as the then unknown opening 1.d4 c5.

Bennoni [sic] gives some examples; but it loses time to White, which deprives Black of all the advantages of a good opening.

(Benoni, oder Vertheidigungen die Gambitzüge im Schache, &c. Von Aaron Reinganum, Frankfort, 1825.

White usually replies 2.d5 in order to gain space, as 2.dxc5 e6 leads to no advantage, and 2.e4 transposes to the Morra Gambit, also promising equality at best.

This form has never attracted serious interest in high-level play, though Alexander Alekhine defeated Efim Bogoljubow with it in one game of their second match, in 1934.

Black's intention is to play ...exd5 and create a queenside pawn majority, whose advance will be supported by a fianchettoed bishop on g7.

While it superficially resembles the Benko Gambit, it has a different strategic goal, that being to initiate counterplay against White's pawn center rather than develop positional pressure on the queen's side.