The answer is both yes and no.
The first thing to understand is that "Christ" is not Jesus' last name. It is a title. The Greek word “Christos” means "Anointed One," or "Messiah." Jesus is His personal name, while Christ describes His God-given role as the promised Savior and King foretold throughout the Old Testament.
When a writer in the New Testament says "Jesus Christ," his emphasis is often on identifying Jesus of Nazareth as the promised Messiah. It is something like saying, "Jesus is the Christ." This concept was the central message of the apostles' preaching.
One of the apostles, Peter, expressed this truth when he declared, "You are the Christ, the Son of the living God" (Matthew 16:16). And again, the Apostle John told his writers that he wrote his Gospel "that you may believe that Jesus is the Christ, the Son of God" (John 20:31).
Now, on the other hand, the expression "Christ Jesus" often places the title first, then draws attention to Jesus' exalted position as the Messiah before mentioning His personal name. This word order appears especially often in the writings of the Apostle Paul.