Altispinax oweni was coined by Friedrich von Huene in 1923 for BMNH R2559: three metatarsals from the Early Jurassic Tunbridge Wells Sand Formation in Cuckfield that Owen had assigned to the herbivorous Hylaeosaurus in 1858. Part of the pile of British Museum remains that Richard Lydekker assigned to Megalosaurus dunkeri in 1888, these foot bones were renamed Megalosaurus oweni by Lydekker a mere year later, and George Olshevsky used them to raise Valdoraptor in 1995. Altispinax parkeri was coined by Friedrich von Huene in 1932 for OUM J.12144: a partial hip, leg and backbones from Jordan's Cliff at Weymouth that he had named Megalosaurus parkeri himself in 1923! In 1964 this material was renamed Metriacanthosaurus by Alick Walker. Altispinax lydekkerhueneorum was coined by S. Pickering in 1995 for BMNH R1828, the name-prompting vertebrae that, after a stint as Acrocanthosaurus altispinax (Paul, 1988), were renamed Becklespinax altispinax (George Olshevsky, 1995). Altispinax lydekkerhueneorum is therefore a junior synonym of Becklespinax altispinax.
Altispinax altispinax was coined in 2003 Oliver Rahaut. The name is ridiculous, and thankfully nothing more than a junior synonym of Becklespinax altispinax, which isn't much better.