Who is the people God took out of the Gentiles for His name?
The people are the church, which is His body—predominantly Gentiles called out from among the nations during this age. Acts 15 records James explaining that God visited the Gentiles to take out a people for His name, and that people is the Body of Christ.
Les explains that in Acts 15, James, who was moderating the meeting, refers back to Peter's declaration about how God at the first visited the Gentiles at the house of Cornelius to take out of them a people for His name. Les then asks what that people is and answers: the church, which is His body. He teaches that for the last 1900 and plus years, the church is being formed by predominantly Gentiles who are being called out from among whatever they are, pagans or whatever, and becoming members of the Body of Christ. Les also notes that as soon as this began, the Jews got envious and opposed it everywhere Paul went, and God put a blindness upon the nation. He reminds listeners that God deals with the Jew on two levels, national and personal, so when He blinds them nationally, that does not take away the personal opportunity for salvation.
Simeon hath declared how God at the first did visit the Gentiles, to take out of them a people for his name.
More Questions
What does the Bible call Gentile believers if not 'My people'?
Apart from the Acts passage where God says He is calling out a people for His name, Gentile believers are more correctly referred to as His 'born ones' rather than as 'My people.'