To whom did "the elder" address the letter of 3 John?

Answer: Gaius

3 John is written "to the beloved Gaius"; it also mentions Diotrephes, who loves to be first, and Demetrius, who is well spoken of.

“The elder, To the beloved Gaius, whom I love in the truth: I have written to the church about this, but Diotrephes, who loves to be first, will not accept our instruction. Demetrius has received a good testimony from everyone, and from the truth itself. We also testify for him, and you know that our testimony is true.”— 3 John 1:1, 1:9, 1:12 (BSB)