Our Gemara discusses the concept that a stolen item can eventually become owned by a thief if it becomes substantially changed (though he still must pay for the object). One of the criteria that establish substantial change is if there is a change in the name and descriptor of the object. This can apply even to arbitrary name changes, such as if an ordinary myrtle branch which is now designated for the mitzvah changes from Asa (Hadassah) to Hoshana (Succah 31a.)

This is true metaphysically as well.  In the process of repentance, the idea of a person changing their name to concretize change in behavior and perspective is recommended:

Rosh Hashana (16b):

וְאָמַר רַבִּי יִצְחָק: אַרְבָּעָה דְּבָרִים מְקָרְעִין גְּזַר דִּינוֹ שֶׁל אָדָם, אֵלּוּ הֵן: צְדָקָה, צְעָקָה, שִׁינּוּי הַשֵּׁם, וְשִׁינּוּי מַעֲשֶׂה…שִׁינּוּי הַשֵּׁם, דִּכְתִיב: ״שָׂרַי אִשְׁתְּךָ לֹא תִקְרָא אֶת שְׁמָהּ שָׂרָי כִּי שָׂרָה שְׁמָהּ״, וּכְתִיב: ״וּבֵרַכְתִּי אוֹתָהּ וְגַם נָתַתִּי מִמֶּנָּה לְךָ בֵּן״. 

And Rabbi Yitzḥak said: A person’s heavenly conviction for punishment is torn up on account of four types of actions. These are: Giving charity, crying out in prayer, a change of one’s name, and a change of one’s deeds for the better. An allusion may be found in Scripture for all of them…a change of one’s name, as it is written: “As for Sarai your wife, you shall not call her name Sarai, but Sarah shall her name be” (Genesis 17:15), and it is written there: “And I will bless her, and I will also give you a son from her” (Genesis 17:16).

This is also codified in halakha (Rama, Shulkhan Arukh YD 335:10):

וכן נהגו לברך חולים בב"ה לקרא להם שם חדש כי שינוי השם קורע גזר דינו

And likewise is it the accepted practice to recite blessings [on behalf of] sick persons, in the Synagogues, to give them an [additional] new name, for a change of name causes an evil decree passed upon man to be canceled.

The Rambam (Teshuva 2:4), endorses this practice too, but adds his own emphasis and interpretation:

מִדַּרְכֵי הַתְּשׁוּבָה לִהְיוֹת הַשָּׁב צוֹעֵק תָּמִיד לִפְנֵי הַשֵּׁם בִּבְכִי וּבְתַחֲנוּנִים וְעוֹשֶׂה צְדָקָה כְּפִי כֹּחוֹ וּמִתְרַחֵק הַרְבֵּה מִן הַדָּבָר שֶׁחָטָא בּוֹ וּמְשַׁנֶּה שְׁמוֹ כְּלוֹמַר אֲנִי אַחֵר וְאֵינִי אוֹתוֹ הָאִישׁ שֶׁעָשָׂה אוֹתָן הַמַּעֲשִׂים וּמְשַׁנֶּה מַעֲשָׂיו כֻּלָּן לְטוֹבָה וּלְדֶרֶךְ יְשָׁרָה

Among the paths of repentance is for the penitent to

a) constantly call out before God, crying and entreating;

b) to perform charity according to his potential;

c) to separate himself far from the object of his sin;

d) to change his name, as if to say "I am a different person and not the same one who sinned;"

e) to change his behavior in its entirety to the good and the path of righteousness;

Notice how the Rambam adds, “as if to say ‘I am a different person and not the same one who sinned’" The point is that changing the name is not magical. Rather it helps express, inspire and maintain a fundamental change that becomes internalized.  The Rambam is often is careful to treat rituals and practices in a rational manner and avoid acting as if they are magical. A most famous example comes from Rambam Hilchos Mezuzah (5:4) which rails against those who write angels’ names inside a Mezuzah, as if it were a talisman. Here too, Rambam wants the focus to be on the internal emotional spiritual work, not the external ritual. As Mishna Taanis (2:1) states in regard to the repentance of Nineveh: 

It is not stated with regard to the people of Nineveh: And God saw their sackcloth and their fasting. Rather, the verse says: “And God saw their deeds, that they had turned from their evil way” (Jonah 3:10). And in the Prophets it says: “And rend your hearts and not your garments, and return to the Lord your God” (Joel 2:13). This teaches that prayer and fasting are insufficient, as one must also repent and amend his ways in practice.

However, we never should underestimate the power of symbolism in emotional and spiritual matters. The power of gifting flowers or jewelry to a lover is the same power as blowing a Ram’s horn to cry out to God, or placing the Shema (a written account of the Yoke of Heaven) on our arms, heads and doorposts (Tefilin and Mezuzos), or even throwing our sins into the water and reciting Tashlich. Humans cannot easily change internal states and attitudes without demonstrating and enacting them symbolically. (For a fundamental discussion on symbolism, psychology and religion, see Moreh Nevukhim III:32 and Chinuch 16) Yet, care must be taken not to treat the practice as an end unto itself, and as some kind of magical ritual. After all, to paraphrase the saying about motivation, “You can lead the horse to water, but you cannot make him say Tashlich.”