Acidaspis spiniger was named by Hall (1847) [≠ Bathyrus spiniger; Kay 1937, p. 300, pl. 9 [? = B. (R.) cf. B. (R.) ingalli]. ≠ Raymondites spiniger; Ludvigsen 1979b, p. 39, fig. 22B, C [= B. (R.) ingalli]. ≠ Raymondites spiniger DeMott 1987, p. 76, pl. 8, figs. 1–9 [ = B. (R.) cf. B. (R.) ingalli].]. Its type specimen is AMNH 854, a cephalon/head, and it is a 3D body fossil.

It was recombined as Bathyurus spiniger by Clarke (1894); it was recombined as Raymondites spiniger by Whittington (1953); it was recombined as Bathyurus (Raymondites) spiniger by Swisher et al. (2015).