Name changes in the Bible indicate a significant change in the life of the person. For example,
Abram became Abraham.
"No longer shall your name be Abram, but your name shall be Abraham;
for I have made you the father of a multitude of nations." (Gen 17:5)
Jacob became Israel.
Then he said, "Your name shall no more be called Jacob, but Israel,
for you have striven with God and with men, and have prevailed." (Gen
32:28)
Simon became Cephas, which means rock.
"So you are Simon the son of John? You shall be called Cephas" (which
means Peter). (John 1:42)
Having said that, it is really up to the individual to take a new name. Usually, they like to take the name of a saint whom they are inspired by.