Answer: There are several individuals in Scripture who have gotten a new name by those other than God. This is usually done for a variety of reasons. For example, as captives in Babylon, Daniel and his three friends were referred to differently when they began to serve King Nebuchadnezzar. Daniel was called Belteshazzar, Mishael was called Meshach, Hananiah was known as Shadrach, and Azariah name changed to Abed-Nego (Daniel 1:6 - 7).
The Bible does mention a few individuals who actually did get a new name directly by God or Jesus Christ. Abram was changed to Abraham (meaning "father of many nations," see Genesis 17:1 - 5) then the Eternal changed his wife's from Sarai to Sarah (which means "mother of many nations," see verses 15 - 16). Jacob, the grandson of Abram (Abraham), was given the name Israel (meaning "someone who prevails with the Eternal," see Genesis 32:24 - 28).
One rather unique example of the Lord giving a new name to humans was when He commanded the prophet Hosea to marry a known whore as a sign of Israel's sin.
"When the Lord first spoke to Israel through Hosea, he said to Hosea, 'Go and get married; your wife will be unfaithful (the KJV has 'a wife of whoredoms' or a wife who is a whore), and your children will be just like her'" (Hosea 1:2)
As children were born to Hosea's "whore wife" the Lord gave each of them a name as a testament against the house of Israel (northern ten tribes). The first child, a boy, was called Jezreel, meaning that He would avenge the blood of Jezreel on the royal house of king Jehu. The second child of the whore, a girl, was called Lo-Ruhamah, because the Lord decided not to be merciful to the house of Israel any longer. The third child, a boy, was given the name Lo-Ammi, which generally means the Eternal no longer considered Israel his people (Hosea 1:3 - 4, 6, 8 - 9, HBFV).
Only four people in the entire New Testament were given a new name. The scriptures tell us that Jesus gave three of these new references during his earthly ministry. Simon, sometime after becoming one of Jesus' original twelve disciples, was called Peter, which means a little stone (John 1:40 - 42). Not many people, however, are aware that Jesus gave the brothers John and James a rather humorous designation of 'the sons of thunder' (Mark 3:13 - 17)!
The fourth person in the New Testament given a new name was Saul, who became Paul. The Bible does not state if God gave him the new reference or not. We do know, however, that he was called Paul sometime after his baptism. The last time 'Saul' (which means "demanded" or "death") is mentioned in the New Testament and the first place where he is called Paul (which means "small" or "little") is in Acts 13. This renaming is mentioned when he performs a major miracle during his first missionary journey.
But Saul, who was also called Paul, being filled with the Holy Spirit, fixed his eyes on him (a false prophet named Bar-jesus) . . . And now behold, the hand of the Lord is upon you (God is going to directly punish you for your disobedience), and you shall be blind . . ." (Acts 13:9, 11)