Well, the Garden of Gethsemane was located at the foot of the Mount of Olives. The Bible says that Jesus is brought from Gethsemane TO Jerusalem, through the Kidron Valley. Would not the Romans already know who Jesus was?
No scripture says that it was the Romans came for Jesus it was the Jewish temple guard.
Matthew
While he was still speaking, Judas, one of the Twelve, arrived. With him was a large crowd armed with swords and clubs, sent from the chief priests and the elders of the people
JohnSo Judas came to the grove, guiding a detachment of soldiers and some officials from the chief priests and Pharisees. They were carrying torches, lanterns and weapons.
LukeAnd Judas went to the chief priests and the officers of the temple guard and discussed with them how he might betray Jesus
While he was still speaking a crowd came up, and the man who was called Judas, one of the Twelve, was leading them. He approached Jesus to kiss him,
MarkJust as he was speaking, Judas, one of the Twelve, appeared. With him was a crowd armed with swords and clubs, sent from the chief priests, the teachers of the law, and the elders.