Green’s Dictionary of Slang

(US) a phr. indicating failure, one has no chance, one is finished, ‘done for’; also abbr. as Dennis.

1839		in Knickerbocker (N.Y.) 383: Carry me on, and his name’s Dennis*! *[Note] A whale’s name is ‘Dennis,’ when he spouts blood.
1878		A.F. Mulford Fighting Indians 64: When he did get after a man, his name was Dennis.
1884		C.F. Lummis letter in Byrkit Letters from the Southwest (1989) 47: He was just mulish enough not to budge, and would have been named ‘Dennis’ in a brief time.
1900		P.G. McLean ‘A Long Shot’ Variety Stage Eng. Plays 🌐 If Stewart gets out of that office, my name’s Dennis.
1903		A. Kleberg Slang Fables from Afar 27: Of course if Browne refused to agree it would be all up the Spout with him or in fewer words his name would be Dennis.
1920		Ade Hand-made Fables 74: Mr. Foster’s name was Dennis X. Mud with about 240 per cent. of the highminded Peers.
1926		in J.F. Dobie Rainbow in Morning (1965) 84: His name is Dennis.
1947		(con. 1870s) F. Weitenkampf Manhattan Kaleidoscope 84: ‘His name is Denis’ implied that one was a goner.