Here the word "them" refers to Paul and Barnabas.
All the multitude
"Everyone" or "The whole group" (See: Acts 15:6)
God had worked
"God had done" or "God had caused"
a people for his name
"Name" here is a metonymy for "God's own purposes." AT: "a people for God's own purposes" (See: rc://en/ta/man/translate/figs-metonymy)