(adjective) : Sōcrătes, is, m., = Σωκράτης.
* The celebrated Greek philosopher: parens philosophiae,Cic. Fin. 2, 1, 1: fons et caput philosophiae,id. de Or. 1, 10, 42: ab Apolline omnium sapientissimus dictus,id. Ac. 1, 4, 16; Plaut. Ps. 1, 5, 50.—Voc. Socrate, bis, Cic. Fragm. p. 477 Orell.—As an appellative, in the plur.: ut exsistant ... Socratae simul et Antisthenae et Platones multi,Gell. 14, 1, 29; cf. Lachm. ad Lucr. 2, p. 50. —Hence, Sōcrătĭcus, a, um, , = Σωκρατικός, of or belonging to Socrates, Socratic: philosophi,Cic. Off. 1, 29, 104: viri,id. Att. 14, 9, 1: domus,Hor. C. 1, 29, 14: sermones,Cic. de Or. 3, 18, 67; Hor. C. 3, 21, 9: lepor subtilitasque,Cic. Rep. 1, 10, 16: chartae,Hor. A. P. 310: sinus,i. e. devoted to philosophy,Pers. 5, 37: Xenophon,Nep. Ages. 1: cinaedi (in reference to Alcibiades, the favorite of Socrates),Juv. 2, 10.—As subst.: Sōcrătĭci, ōrum, m., the followers or disciples of Socrates, Cic. de Or. 3, 16, 61 sq.; id. Off. 1, 1, 2 et saep.
* A Greek painter, Plin. 35, 11, 40, § 137.
* A Greek sculptor, Plin. 36, 5, 4, § 32.

Personal name
Confirmed occurences in the Roman Empire:

• M. Aurelius Papirius Socrates (Masc), ref: PIR A 1568 | PIR ID2628
• D. Iunius Arabianus Socrates (Masc, eques), ref: SEG 37, 1539 | PIR ID7915
• Papirius Socrates (Masc, eques), ref: PIR P 0120 | PIR ID10106
• Pinius Socrates (eques), ref: P. Col. V 1 verso 5, 11 | PIR ID14747