The purpose of this article is to explain the concept of name change in Judaism. First, it is important to understand that changing one's name is not a way to resolve the problems and difficulties a person may be experiencing.
On the other hand, the concept that a name change influences a person's life is a Jewish concept that appears in our sources. It is present from the very beginning of the Torah narrative, when the first man named each creature (Genesis 2:20).
(The idea, as explained in Hasidic thought, is not that the first man gave arbitrary names to each creature—that is, he called the cat a cat and the dog a dog—but rather that the name of a creature is the channel of energy through which God creates and sustains everything in the entire universe. Thus, the first man revealed from within each creature the letters of the Hebrew alphabet, which are the channel of creation and life for each thing. The first man was able to see the name of each creature...)
And passing through Abraham our patriarch, who was originally called Avram, and God changed his name so that he would have children (just as Sarah, our matriarch, in the same way: originally she was called Sarai and had no children, and she became known as Sarah). See Rashi's commentary on Genesis 15:5.
The Talmud in Rosh Hashanah 16b explains that changing one's name is one of the things that breaks negative decrees against a person. Some explain that this is because changing one's name expresses the person's will to change their behavior, etc. (see Laws of Repentance, chapter 2, law 4).
On the other hand, the Rashba (Shut HaRashba 5:48) opines that a name change, regardless of the person's behavior, generates a change in the person's life force. Similarly, the Zohar (1, 15-16) presents the idea that a name change generates changes in the person's concrete life.
In practice, in the Shulchan Aruch (Code of Jewish law) the concept of name change is specifically listed as a tool in helping sick people (Yoreh Dea 335:10, Rama's note).
In conclusion, if a person truly wishes to change their name, they can do so, and of course, they shouldn't expect that to solve their life's problems but should instead work to improve it.
In any case, it's important to know that what truly establishes a person's name is how that person is called by others (friends, family, etc.). This is more important than how that person identifies themselves or how they are referred to when their name is read in the Torah. If a person changes their name but no one uses that name, they have accomplished nothing with the name change.
Regarding Bnei Noach, many ask whether to adopt a Hebrew name. Based on what has been explained, there is no legal reason why they should change or add a Hebrew name. It is not part of Noahide identity, nor does it enhance their connection with the Almighty. The Talmud itself lists dozens of non-Jewish names, and nowhere does it suggest they change their name to a Hebrew one. This does not mean that changing their name is prohibited, but simply that it is not forbidden.