The verse states in the Book of Mishlei (10:7), "The memory of a Tzadik is a blessing, and the name of the wicked shall rot." The Gemara derives from the second half of this verse – "the name of the wicked shall rot" – that when one mentions the name of a wicked person, he must curse that person's name, because the name itself is associated with the evil qualities of the individual. This concept underlies the widespread practice for children to make noise upon hearing the name "Haman" during the Megilla reading, as we are enjoined to denigrate the name associated with a wicked individual.
For this reason, one must ensure not to give his child the name of a wicked person. The Gemara tells of a child whose parents named him Do'eg, the name of a wicked person who lived during the time of King Shaul, and terrible misfortune befell this child as a result. Furthermore, the Chatam Sofer (Rabbi Moshe Sofer, Hungary, 1762-1839) commented, Helek 4:22, that Korach, who led a mutiny against the authority of Moshe Rabbenu in the wilderness, was named after Esav's son Korach (Bereishit 36:14), and because he was given the name of a wicked person, that contributed in him becoming a sinner.
One might ask, if, indeed, naming a child after a sinful person has very negative repercussions for his character, how is it that one of the greatest Tanna'im was named Rabbi Yishmael? Yishmael, Avraham's first son, was a sinner; how could somebody named "Yishmael" emerge as one of the most important figures in the Talmud?
Some answered that Yishmael repented before his death, and so his name is no longer associated with sin and immorality. Furthermore, the Chid"a (Rabbi Chayim Yosef David Azulai, Israel, 1724-1806) in his sefer ‘Shem HaGedolim’ explains that if a name is intrinsically meaningful and appropriate, then we may disregard the fact that it had been the name of a wicked person. The name "Yishmael" means "God shall hear" our prayers, and therefore it may be used and will not adversely affect the child's character, despite the fact that it had been the name of an evil person.
The Chid"a applies this rule also to the name "Eliezer," with which Moshe named his second son. This had been the name of Avraham's servant, whom the Sages describe in one source as "cursed." Moshe was nevertheless justified in using this name for his son because of its meaning: "My God assists." Given the religious meaning and significance of the name Eliezer, it is not directly associated with the "cursed" person who had been known by that name.
The Chid"a also cites the ruling of the Mabit (Rabbi Moshe of Trani, Turkey-Israel, 1505-1580) that one should not name his child after personalities that lived before Avraham Avinu. Avraham Avinu began the period of "Jewish names," and it is therefore inappropriate to use the name of somebody who lived before Avraham in naming one's child. Thus, one who wishes to name his child "Noach" or "Adam" should first consult with his Rabbi for guidance.
Finally, the Chid"a presents a list of names that one should not use when conducting a "Shinui Ha'shem," when one changes a person's name in situations of illness, Heaven forbid. Once again, one who wishes to change a person’s name should consult with his Rabbi for guidance.
In general, choosing a name for one's child is a most serious matter that must not be taken lightly, given the name's profound impact upon a child's character. One must therefore choose a name very carefully and consult with his Rabbi to ensure that a suitable and appropriate name is selected.
Summary: Extreme care must be taken when selecting a name for one's child. One should not name a child after a wicked person, unless the name is intrinsically meaningful and appropriate – such as in the cases of Yishmael and Eliezer. One who wishes to name a child after a Biblical personality from before the time of Avraham Avinu – such as Adam or Noach – must first consult with a Rabbi. Likewise, one who wishes to change a child's name due to illness should first consult with his Rabbi to receive proper guidance.
