This phrase and similar phrases (in Jesus, In Christ, etc) refers to two very different circumstances. One, we believe in Him, meaning we have information of Christ (sinless sacrifice, Son of God, Savior, etc) which we believe is true and therefore have committed to follow Him and serve Him. The action is ours to take, or not take, and God decides whether our action will be credited as righteousness or not.
The second meaning of "in Him" refers to our spiritual location, within Christ or within Adam. So when you see the phrase, consider which of the two usages is in view.
Acts of the Apostles 19:4
Paul said, “John baptized with a baptism of repentance, telling the people to believe in Him who was coming after him, that is, in Jesus.”
Here the idea is what we hold as true, i.e Christ is our Lord and Savior.
2 Corinthians 5:21
He made Him, who knew no sin, a sin offering in our behalf, so that we might become the righteousness of God in Him.
Here the idea is we become the righteousness of God when placed within Him.
The second meaning of "in Him" refers to our spiritual location, within Christ or within Adam. So when you see the phrase, consider which of the two usages is in view.
Acts of the Apostles 19:4
Paul said, “John baptized with a baptism of repentance, telling the people to believe in Him who was coming after him, that is, in Jesus.”
Here the idea is what we hold as true, i.e Christ is our Lord and Savior.
2 Corinthians 5:21
He made Him, who knew no sin, a sin offering in our behalf, so that we might become the righteousness of God in Him.
Here the idea is we become the righteousness of God when placed within Him.