Names are important to God. (Trust me that it's an entire sermon to just work through the scriptural principle of the progressive revelation of the name of God, consider that saved for another day.) We see that in bible times people also took names very seriously, sadly not something that has survived the passage of time, with modern names selected for the most random of reasons and from the most random of sources.

In his interactions with humanity, we see that God influenced many names, changing some and re-emphasizing others. The classic example of name changing would be that of Abram and Sarai who he renamed to Abraham and Sarah (Genesis 17:5, 15-16). As God changed the directions of their lives, he gave them new names that would match their newfound standing.

The foremost example of a re-emphasis of names is often wrongly thought to be a renaming. People often believe that Paul was renamed from Saul to Paul, as we see him called Saul up to a point and thereafter known as Paul. He already had both names (Acts 13:9), so it was in fact a re-emphasis. The reason for this is that while Paul was a Hebrew (Philippians 3:5), he was also a Roman citizen (Acts 22:27). As a Pharisee, his Hebrew name of Saul was his first choice. The dislike, bordering on hatred, of the Romans among the Jews would have limited his ability to operate as a religious leader of the Jews if he had gone by his Roman name Paul. Upon his appointment as the apostle to the Gentiles (Romans 11:13), many of whom were Roman or highly influenced by Roman culture and who often disliked Jews as much as the Jews disliked them, Paul found more acceptance of his teaching when favoring his Roman identity. Interestingly, the switch of usage from Saul to Paul was not God ordained. Paul chose the emphasis change for the afore-mentioned reasons.

The switch of emphasis of Simon to Peter was directed by God (Matthew 16:16-18). Simon's full name was Simon Peter and he did in fact use that name in his second epistle, but Jesus emphasized Peter because it means rock and corresponded to Peter's revelation of the messiahship of Jesus, which is the rock and foundation upon which the coming church would be built.