Step 1: Map the blood supply. The lateral medulla draws its supply from the PICA, the largest branch of the vertebral artery. A clot here starves the lateral wedge of the medulla. Step 2: Clinically this gives the classic lateral medullary picture - ipsilateral facial sensory loss, Horner sign, ataxia, dysphagia, with contralateral loss of pain and temperature over the body. The eponym for this is Wallenberg syndrome, first described in 1895. Step 3: Contrast with the medial medulla, supplied by the anterior spinal artery; its occlusion produces medial medullary syndrome, which carries the alternative names inferior alternating syndrome, hypoglossal alternating hemiplegia and Dejerine syndrome. Since the question asks about PICA, all three medial names are excluded. Step 4: Therefore the only correct match for PICA thrombosis is the lateral medullary or Wallenberg syndrome. \[\boxed{\text{Wallenberg syndrome}}\]