Lophocephalus parki was named by Benham (1937) [Otago University]. Its type specimen is OU C.'34.8, a skull, and it is a 3D body fossil. Its type locality is Milburn Quarry, which is in a Chattian carbonate limestone in the Milburn Limestone Formation of New Zealand.

It was recombined as Mauicetus parki by Benham (1939), Benham (1942), Harland et al. (1967), Keyes (1973), Fordyce (1980), Fordyce (1991), Fordyce (1992), Fordyce (2005), Fordyce and Roberts (2009), Marx and Fordyce (2015), Robinson et al. (2024).