Possession shouldn't be thought of as a viable use for the dative at all. There is a category sometimes called "Dative of the Possessor," but if you saw it, and you understood that the noun is in the dative case, you'd easily make sense of the construction without thinking of possession. There are 2 instances that come close to "possession," though the first one seems pretty dubious to me. (I'm leaning on Smyth's explanation here).
1. Set ways of introducing someone's name. So ὄνομα αὐτῷ ἐστιν Ἀγάθων = "his name is Agathon." But I wouldn't say this is a "use" of the dative, so much as it's a solidified idiomatic manner of introducing someone.
2. If a noun is already in the genitive, and then something is attributed to it as a possession, then the second noun (the one that is possessed) goes into the dative. So: τῶν αὐτοῖς ξυμμάχων = "his allies." This make sense in a "sequence of cases" way (i.e., analogous to "sequence of tenses"). But obviously if you saw it, the meaning would be clear as soon as you thought "the allies in his case," or something like that (i.e., a more more typically "dative" construal).