John uses the plural we. Further on in the letter he always uses the singular I.
In the pronoun we
it can be seen that he, together with others, was an eye and ear witness to Christ’s appearance on earth. It shows his connection with the other apostles. Their desire is for the church to believe and keep this testimony that they brought to the world at the command of Christ.
When we look at the second part of this verse, we see a striking difference in translations. John makes it clear that it is his goal that by living together based on the unified testimony of the ear and eye witnesses, people are truly connected to one another and truly belong to Christ and God as Father, with the effect “that our/your joy may be complete.” In Greek, the difference between our and your is minimal: hēmōn/hymōn. There is a difference in the manuscripts on this point. It seems to me that as you read John’s letters further that “our joy” is the better choice. Yet both make good sense.
This paragraph will explain why it makes proper sense when we read “our joy” (ESV, NASB, NIV). John is concerned about developments in the churches. He sees how the temptation is coming upon believers to believe in Christ in a different way, to follow a false doctrine. John also makes it clear in other places in his letters that it is precisely this holding on to sound doctrine that makes him so happy. We read this in:
2 John 1:4:
I rejoiced greatly to find some of your children walking in the truth, just as we were commanded by the Father.
3 John 1:3–4:
For I rejoiced greatly when the brothers came and testified to your truth, as indeed you are walking in the truth. I have no greater joy than to hear that my children are walking in the truth.
John’s joy becomes even more pronounced when he hears and sees that the believers hold on to the word he brought and stay with the true gospel. In the face of worry, that makes him intensely happy.
It also makes good sense when we read with, for example, the (N)KJV: “your joy.” True joy that endures can only exist when we hear the gospel according to God’s Word again and again, full of wonder. When we entrust ourselves to Christ as the One who reconciled us to the Father by taking our guilt upon himself. Being a child of God through Christ’s sacrifice really makes us happy! We can relax and have peace as we hear the voice of our Saviour. And we may hear his voice together with others: the voice of the Good Shepherd. In this way he is in our midst. And your joy is complete. To be able to find your rest in Christ alone! Let that be our joy and let us not ever allow this to be taken away from us. Give no opportunity to the devil—also in this matter!
4 And we are writing these things so that our joy may be complete.