Exegesis:

hoti marks here the beginning of direct speech.

oudeis estin ek tēs suggeneias sou hos kaleitai tō onomati toutō ‘there is nobody of your relatives who is called by that name.’ ek tēs suggeneias sou ‘of your relatives’ goes with oudeis and stands for a partitive genitive, meaning ‘belonging to,’ or ‘being a part of.’

suggeneia ‘kinship,’ here in the concrete and collective sense ‘relatives,’ cf. on v. 36 (suggenis).

Translation:

None of your kindred. The partitive, often expressed by prepositions, cf. “in” (New English Bible), ‘among’ (Bahasa Indonesia), may also be indicated by simple juxtaposition of the collective noun and the reference to the part, e.g. ‘all your-relatives no one’ (Javanese, Toraja-Sa’dan). For kindred cf. on “kinsfolk” in v. 58.

None … is called by this name, or, ‘not one is called/named that way’ (Apache), “there is no one … who bears that name” (An American Translation), ‘no one … we (inclus.) call thus, or, by that name.’

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.