Belonostomus acutus was named by Agassiz (1843). Its type specimen is BMNH P4268, P961a and is a compression fossil. Its type locality is Whitby (Enniskillen coll), which is in a Toarcian marine siliciclastic in the United Kingdom.

It was recombined as Belonorhynchus acutus by Woodward (1895); it was recombined as Acidorhynchus acutus by Neuman and Wilson (1985); it was recombined as Saurorhynchus acutus by Gardiner (1960), Kogan (2016), Maxwell and Stumpf (2017), Maxwell and Martindale (2017).