It is Jewish tradition to add an extra name to someone when they are gravely ill. However, this is something to be done with caution, as the following reported rabbinic advice indicates.
People add names to those who are gravelly ill. Doing so is thought to ward of the Angel of Death by changing the person – a person’s mazel is somehow connected to his name. By changing the person’s name, you are in effect creating a new person with a different mazel than the person he was previously.
Kikar is reporting that due to the gravity of Rav Elyashiv’s illness, and his continually deteriorating situation, Rav Kanievsky was asked about the possibility of adding a name to Rav Elyashiv’s name.
Rav Kanievsky paskened that they should not add the name. Doing so turns the person somehow into a new person upon whom the illness was not decreed. However, with someone like Rav Elyashiv, all his merits are because of his name – if they would change his name and turn him into a new person with a new mazel, doing so might cancel out all his merits he has accumulated over his lifetime.
Rav Kanievsky add that this is the psak Rav Elyashiv himself gave many years ago when Rav Moshe Feinstein was ill and they were considering adding a name.
The ramifications of this are astounding. If it really creates a new person to the point that he would lose all his previous merits, would he still get rewarded for his good deeds after passing if his name had been changed? What about the other way – can someone who was not so good change his name in order to start over with a clean slate or to avoid punishment in the afterworld? Could a person change his name every time he does something wrong – it would make repentance so much easier! (civilly I think one can only change his name every 7 years)