3 witnesses of Christ here, and 2 further echoes from the reading.
Then remembered I the word of the Lord, how that he said, John indeed baptized with water; but ye shall be baptized with the Holy Ghost. Acts 11:16
Peter remembers the risen Lord's own words promising the baptism of the Holy Ghost. Seeing the Gentiles receive that gift showed him Jesus meant them too.
Forasmuch then as God gave them the like gift as he did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God? Acts 11:17
The gift of the Holy Ghost follows faith in the Lord Jesus Christ, whether the believer is a Jew or a Gentile.
How we know: the verse itself names Him · a Church study aid lists it
And some of them were men of Cyprus and Cyrene, which, when they were come to Antioch, spake unto the Grecians, preaching the LORD Jesus. Acts 11:20–21
Disciples from Cyprus and Cyrene preach the Lord Jesus to Greeks in Antioch, and a great number turn to Him. "The Lord" here is Jesus, the One they preached.
How we know: the verse itself names Him · a Church study aid lists it
Who, when he came, and had seen the grace of God, was glad, and exhorted them all, that with purpose of heart they would cleave unto the Lord. Acts 11:23–24
Barnabas teaches the new converts to hold fast to the Lord Jesus with real purpose of heart. Conversion is being joined to Christ, not just to a group.
Christians — those who belong to Christ, the Anointed One
And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people. And the disciples were called Christians first in Antioch. Acts 11:26
The followers of Jesus become known by His name. The name "Christians" shows that their identity comes from Christ.
How we know: a footnote points to Him · a Church study aid lists it