It seems that before Andrew could introduce his brother Christ spoke to him. There must have been some wonder in Simon that Jesus knew his name.
We do not all receive new names when we become believers in Christ. But we do receive what the new name pictures and depicts: a new nature, a new character. Some of it is given at once, much of it is added down life’s pathway. When we come to Christ we are completely converted, but then there is a development in character, and substance, and understanding, and communion, and usefulness to Christ.