Mark 14:51,52 Now a certain young man followed Him, having a linen cloth thrown around his naked body. And the young men laid hold of him, 52 and he left the linen cloth and fled from them naked.
He is almost certainly John Mark, who wrote the Gospel of Mark.
Whoever it was must have followed Jesus to Gethsemane from the ‘upper room’ of the last supper. We learn that John Mark lived in Jerusalem with his mother Mary.
Acts 12:12 So, when he (Peter) had considered this, he came to the house of Mary, the mother of John whose surname was Mark, where many were gathered together praying.
It seems reasonable to conclude that the ‘upper room’ was held in Mary’s house and when Jesus and his disciples left, John Mark got out of bed to follow them. In his haste, he didn’t have time to get properly dressed and just wrapped himself in a linen cloth.
John Mark subsequently went with Paul and Barnabas on their first missionary journey.
Acts 12:25 And Barnabas and Saul returned from Jerusalem, when they had fulfilled their ministry, and took with them John, whose surname was Mark.
Perhaps because of his youth, he gave up and returned home halfway. Paul was disappointed in him and didn’t want to take him on their next missionary journey, but Barnabas was intent on giving him another chance. In the end they split with Barnabas taking John with him and Paul choosing Silas.
Acts 15:37-41 And Barnabas determined to take with them John, whose surname was Mark. 38 But Paul insisted that they should not take with them the one who had departed from them in Pamphylia, and had not gone with them to the work. 39 Then the contention became so sharp that they parted from one another. And so Barnabas took Mark and sailed to Cyprus; 40 but Paul chose Silas and departed, being commended by the brethren to the grace of God. 41 And he went through Syria and Cilicia, strengthening the churches.
I hope you find this helpful.