dative of the possessor

So with verbs of thinking and perceiving: τὸν ἀγαθὸν ἄρχοντα βλέποντα νόμον ἀνθρώποις ἐνόμισεν Cyrus considered that a good ruler was a living law to man X. C. 8.1.22, θαρροῦσι μάλιστα πολέμιοι, ὅταν τοῖς ἐναντίοις πρᾱ́γματα πυνθάνωνται the enemy are most courageous when they learn that the forces opposed to them are in trouble X. Hipp. 5.8.

In the phrase ὄνομά (ἐστί) τινι the name is put in the same case as ὄνομα. Thus, ἔδοξα ἀκοῦσαι ὄνομα αὐτῷ εἶναι Ἀγάθωνα I thought I heard his name was Agathon P. Pr. 315e. ὄνομά μοί ἐστι and ὄνομα (ἐπωνυμίᾱν) ἔχω are treated as the passives of ὀνομάζω. Cp. 1322 a.

Here belong the phrases (1) τί (ἐστιν) ἐμοὶ καὶ σοί; what have I to do with thee?; cp. τί τῷ νόμῳ καὶ τῇ βασάνῳ; what have the law and torture in common? D. 29.36. (2) τί ταῦτ᾽ ἐμοί; what have I to do with this? D. 54.17. (3) τί ἐμοὶ πλέον; what gain have I? X. C. 5.5.34.

The dative of the possessor denotes that something is at the disposal of a person or has fallen to his share temporarily. The genitive of possession lays stress on the person who owns something. The dative answers the question what is it that he has?, the genitive answers the question who is it that has something? The uses of the two cases are often parallel, but not interchangeable. Thus, in Κῦρος, οὗ σὺ ἔσει τὸ ἀπὸ τοῦδε Cyrus, to whom you will henceforth belong X. C. 5.1.6, ᾧ would be inappropriate. With a noun in the genitive the dative of the possessor is used (τῶν ἑκατέροις ξυμμάχων T. 2.1); with a noun in the dative, the genitive of the possessor (τοῖς ἑαυτῶν ξυμμάχοις 1. 18).