Three letters in the epistolary corpus of Gregory of Nazianzus are addressed to the sophist Eustochius, an old friend of the bishop and teacher of rhetoric (Ep. 189 – 191). These texts concern the education of Gregory’s great-nephew Nicobolus and the rivalry between the school of Eustochius and that of Stagirius. This hostility links the teaching of Eustochius to the cultural and social context of Caesarea in Cappadocia, but few other details are known about his life and literary activity. He has often been identified with the addressee of Julian’s Ep. 41 (concerning the consular celebrations of 363). However, there is another possibility available. Indeed, another namesake can be linked to the same context of Gregory’s friend. The Suda mentions an Eustochius (s.v. Εὐστόχιος Καππαδόκης), and attributes to his authorship a work on emperor Constans (τὰ κατὰ Κώνσταντα τὸν βασιλέα) and an antiquarian work about Cappadocia (᾽Αρχαιολογία Καππαδοκίας). An identification of this sophist with the fellow student of Gregory has been proposed, but lacks a complete and deep examination. The aim of my paper is to verify this theory through an analysis of all the evidence involved (in particular, some passages of Gregory’s letters). In my opinion, such a test will improve what we know about Gregory and one of his epistolary contacts. In addition, it will increase our knowledge of the literary development of Cappadocia in the fourth century.