see in that the Christians did begin to gather together on Sunday in the New Testament.
[
Act 20:7 NKJV] 7 Now on the first [day] of the week, when the disciples came together to break bread, Paul, ready to depart the next day, spoke to them and continued his message until midnight.
(labor and traders used to get their gain daily, so this is an actual Christian gathering)
[1Co 16:2 NKJV] 2 On the first [day] of the week let each one of you lay something aside, storing up as he may prosper, that there be no collections when I come.
[
Rev 1:10 NKJV] 10 I was in the Spirit on the Lord's Day, and I heard behind me a loud voice, as of a trumpet,
The name "Lord's Day" (different in greek to the "Day of the Lord") began to be used to refer to Sunday. As you can see in the early christian writings. So, it is probably correct to say that John was talking about Sunday.
Pulpit Commentary: The phrase had not yet become common in A.D. , as is shown from St. Paul writing, "on the first of the week" (
1 Corinthians 16:2), the usual expression in the Gospels and Acts (
Matthew 28:1;
Mark 16:2;
Luke 24:1;
John 20:19;
Acts 20:7; comp.
Mark 16:9). But from Ignatius onwards, we have a complete chain of evidence that ἡ Κυριακή became the regular Christian name for the first day of the week; and Κυριακή is still the name of Sunday in the Levant. "No longer observing sabbaths, but fashioning their lives after the Lord's day" (Ign., 'Magn.,' 9.). Melito, Bishop of Sardis (A.D. 170), wrote a treatise περί Κυριακῆς (Eusebius, 'Hist. Eccl.,' IV. 26:2). Dionysius of Corinth (A.D. 175), in an epistle to the Romans, mentions that the Church of Corinth is that day keeping the Lord's holy day (Eusebius, 'Hist. Eccl.,' IV. 23:11). Comp. also Clem. Alex., 'Strom.,' VII. 12:98 (p. 377, Potter); Tertull., 'De Con.,' 3. and 'De Idol.,' 14, where Dominicus dies is obviously a translation of Κυριακὴ ἡμέρα; and fragment 7 of the lost works of Irenaeus.
I wonder if the gathering on the first day of the week was because the first Christians were Jews even the ones in exile, and they observed the Sabbath (Friday 6pm to Saturday 6pm), it was natural to keep going (since they didn't work that day) and gather with other Christians at homes after 6pm (Sunday at that point). Hence, Paul teaching until midnight "Paul, ready to depart the next day, spoke to them and continued his message until midnight."
Apparently, it became a day dedicated to seek the Lord together and do the Lord's Supper, that would work for both the Jews keeping the Sabbath and for the Gentiles.