Heidegger's Bible Handbook: 2 John: Recipients

2. It is inscribed to an elect Lady, not a Church, but an individual matron, and to her children.

The Epistle is inscribed ἐκλεκτῇ κυρίᾳ καὶ τοῖς τέκνοις αὐτῆς, to the elect Lady, and her children. Some ineptly, and Hammond among others, by the elect Lady understand the Christian Church; because both κυρία/kuria/lady among the Athenians, and Curia among the Romans, signifies Church. For, he attributes to this elect Lady children, walking in the truth, to whom he promises that he is going to come, with the children of her sister also greeted, verses 12, 13. This is more rightly understood of a certain matron, a believing and honest Lady. And κυρία is able to be the same thing as the Syriac מרתא/ Martha, which means Lady. Unless perhaps she was distinguished with this name on account of power, servants subject to her, or marriage to some great man. But she is also called ἐκλεκτὴ/elect, not so much by reason of her excellent virtues, as of eternal ἐκλογῆς/election. Just as also Peter writes to the ἐκλεκτοὺς/elect.[1]

[1] 1 Peter 1:1: “Peter, an apostle of Jesus Christ, to the elect strangers scattered (ἐκλεκτοῖς παρεπιδήμοις διασπορᾶς) throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia…”