And - another disciple - Not That other disciple, for the article is omitted by AD, two others; some editions; Syriac, Persic, Gothic, and Nonnus. So the Vulgate is to be understood. There are many conjectures who this disciple was: Jerome, Chrysostom, Theophylact, Nonnus, Lyra, Erasmus, Piscator, and others, say it was John. It is true John frequently mentions himself in the third person; but then he has always, whom Jesus loved, as in John 13:23; John 19:26; John 21:7, John 21:20, except in John 19:35, where he has plainly pointed out himself as writer of this Gospel; but, in the place before us, he has mentioned no circumstance by which that disciple may be known to be John. To this may be added that John being not only a Galilean, but a fisherman by trade, it is not likely that he should have been known to the high priest, as it is here said of that disciple who followed Jesus with Peter. See Bishop Pearce and Calmet. The conjecture of Grotius is the most likely: viz. that it was the person at whose house Jesus had supped. St. Augustin, Tract. 113, speaks like a man of sound sense: We should not decide hastily, says he, on a subject concerning which the Scripture is silent.

Simon.

Matthew 26:58 But Peter followed him afar off to the high priest's palace, and went in, and sat with the servants, to see the end.

*etc:

Mark 14:54 And Peter followed him afar off, even into the palace of the high priest: and he sat with the servants, and warmed himself at the fire.

Luke 22:54 Then took they him, and led him, and brought him into the high priest's house. And Peter followed afar off.

Art Thou a King?
'Then led they Jesus from Caiaphas unto the hall of judgment: and it was early; and they themselves went not into the judgment hall, lest they should be defiled; but that they might eat the passover. Pilate then went out unto them, and said, What accusation bring ye against this Man? They answered and said unto him, If He were not a malefactor, we would not have delivered Him up unto thee. Then said Pilate unto them, Take ye Him, and judge Him according to your law. The Jews therefore said unto him, …
Alexander Maclaren—Expositions of Holy Scripture: St. John Chaps. XV to XXI

The Arrest.
"When Jesus had spoken these words, He went forth with His disciples over the brook Kidron, where was a garden, into the which He entered, Himself and His disciples. Now Judas also, which betrayed Him, knew the place: for Jesus ofttimes resorted thither with His disciples. Judas then, having received the band of soldiers, and officers from the chief priests and the Pharisees, cometh thither with lanterns and torches and weapons. Jesus therefore, knowing all the things that were coming upon Him, went …
Marcus Dods—The Expositor's Bible: The Gospel of St John, Vol. II

Peter's Denial and Repentance.
"So the band and the chief captain, and the officers of the Jews, seized Jesus and bound Him, and led Him to Annas first; for he was father-in-law to Caiaphas, which was high priest that year. Now Caiaphas was he which gave counsel to the Jews, that it was expedient that one man should die for the people. And Simon Peter followed Jesus, and so did another disciple. Now that disciple was known unto the high priest, and entered in with Jesus into the court of the high priest; but Peter was standing …
Marcus Dods—The Expositor's Bible: The Gospel of St John, Vol. II