1) The Sages teach us that one’s Neshama and his mission in life is connected and hinted within his name. As the sefer Bris Avos (8:47), citing the Arizal, writes, “It is a mere misconception that a parent names a child arbitrarily. Rather, it is with Divine inspiration. For it is known before Him the purpose and (eventual) actions of the child, be it for the good or for the bad, all of which are concealed in his name. Each letter of the name reveals more and more about the person. Even if one finds an evil person with a name destined for the righteous, it is clear that contained in him is a small spark of goodness”.
2) The gemara (Rosh Hashana 16b) lists four methods of changing a heavenly decree that has been issued against a person. The methods listed include giving charity, crying out to God, changing one’s deeds, and changing his name. Based on this gemara, the Rema (Yoreh Deah 338:10) records the custom to change the name of a dangerously ill person in an attempt to change the decree against him and save his life. The reason that changing the name can be effective is that one is altering the choleh’s spiritual makeup and thus changing his mazal. (See Minchas Chein on Rambam Teshuva 2:4, Sefer V’Ela Shmos by Rav Yaakov Hillel shlit”a and Sefer Otzar Dinim V’Hanhagim page 428) It goes without saying that one should not change one’s name unless he spoke to a prominent posek who understands both Halacha and Kabbalah.
3) The Gemara states that one should “change” his name and indeed Harav Yaakov Hillel shlit”a (V’Ela Shmos) feels that one must entirely change his name and merely adding a name is not effective. However, the overwhelming majority of opinions maintain that one should not change the name, but rather add a name. This is especially true according to the Ari z”l that one’s Neshama is connected to one’s name, one should therefore not uproot his original name entirely. (Gesher Hachaim 1:3:4, Taamei Haminhagim page 105, Yabia Omer 5 Y.D. 21:3 and Dvar Moshe Teumim 48)
4) The Lubavitcher Rebbe zt”l (Shaarei Halacha U’Minhag vol. 3 page 3oo) writes that since the name of a person is the “spiritual pipeline” connecting the soul to the body one should not add a name unless it is extremely necessary”. The Sefer chassidim (245) rules that one may only change the name for a choleh who is in a life threatening situation. Once again, one should only alter the name after consulting a competent Halachis authority.
5) The new name should be added before the original name. For example if his name is Moshe and the are adding the name Refael, his name become Refael Moshe and not Moshe Refael. (Gesher Hachaim 1 page 31)
6) If one recovers from the illness for 30 days his additional name remains with him for the rest of his life (for aliyos, kesubos etc.). If, however, he did not recover for 30 days his additional name is not used on his tombstone. (Gesher Hachaim ibid.)
7) The Chida (Sefer D’vash Lefi) writes that when adding a name for a woman, one should not add the names Rachel, Batsheva, Tamar, or Leah, but should instead choose Chanah, Sarah, or Yocheved.
8) The poskim debate whether a person needs to re-write the Kesubah after his name is added. According to Harav Yitzchak Weiss zt”l a new Kesubah is needed, while according to Harav Elyashiv zt”l and Harav Wosner zt”l one need not write a second Kesubah. (See Hanisuin K’Hilchosom page 357 and Shevet Halevi 8:286)