In the phrase «Τί σοι ἐστιν ὄνομά» in Luke 8:30, the 2nd person personal pronoun σοι is declined in the dative case. Literally translated as “What is the name to you?”, it is understood as “What is your name?” This type of dative is known as the dative of possession.1 This Greek construction is not a Hebraism, but Hebrew does share a similar construction when it uses the prefixed ל (lamed) to indicate possession.2 Indeed, Donaldson wrote, “In Hebrew there is no other means of expressing the verb “to have” than by this use of the dative.”3
1 Blass, p. 111–112, §37, 3.; Bullions, p. 222–223, §148; Crosby, p. 248–249, §459; Donaldson, p. 494, §dd; Goodwin, p. 248, §1173; Wallace, p. 149, §7; Winer, p. 264
2 For example, in Psa. 50:10: כִּי לִי כָל חַיְתוֹ יָעַר—literally, “For every beast of the forest is to me,” but understood as, “For every beast of the forest is mine.” Also, cf. Gesenius, Hebrew Grammar, p. 419–420, §129; Gesenius, Gesenius’s Hebrew and Chaldee Lexicon to the Old Testament Scriptures, p. 422, lamed, 4., b.; HALOT, p. 509, lamed, 11.
3 Donaldson, p. 494, §dd
Regarding the difference between the dative of possession and genitive of possession, Herbert Weir Smyth wrote,4
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. ... 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.).
However, Peter Bullions wrote,5
it appears often to have been a matter of indifference which of them was used; so much so, that a sentence sometimes begins with the one construction and ends with the other.
4 Smyth, p. 342, §1480
5 Bullions, p. 222–223, §148
Blass, Friedrich Wilhelm. Grammar of New Testament Greek. Trans. Thackeray, Henry St. John. 2nd ed. London: Macmillan, 1905.
Bullions, Peter. The Principles of Greek Grammar: Comprising the Substance of the Most Approved Greek Grammars Extant, for the Use of Schools and Colleges. 21st ed. New York: Pratt, 1851.
Crosby, Alpheus. A Compendious Grammar of the Greek Language. New York: Woolworth, 1871.
Donaldson, John William. A Complete Greek Grammar for the Use of Students. 3rd ed. Cambridge: Deighton, 1862.
Gesenius, Heinrich Friedrich Wilhelm. Gesenius’s Hebrew and Chaldee Lexicon to the Old Testament Scriptures. Trans. Tregelles, Samuel Prideaux. London: Bagster, 1860.
Goodwin, William Watson. A Greek Grammar. Boston: Ginn, 1895.
Gesenius, Heinrich Friedrich Wilhelm. Hebrew Grammar. 2nd ed. Trans. Cowley, Arthur Ernest. Oxford: Clarendon, 1910.
Koehler, Ludwig; Baumgartner, Walter. A Hebrew and Aramaic Lexicon of the Old Testament. Trans. Richardson, M. E. J. Ed. Baumgartner, Walter; Stamm, Johann Jakob. Leiden: Brill, 2002.
Smyth, Herbert Weir. A Greek Grammar for Colleges. New York: American Book, 1920.
Wallace, Daniel B. Greek Grammar, Beyond the Basics: An Exegetical Syntax of the New Testament. Grand Rapids: Zondervan, 1996.
Winer, George Benedikt. A Treatise on the Grammar of New Testament Greek. 3rd ed. Trans. Moulton, William Fiddian. Edinburgh: Clark, 1882.