A person’s name is linked to his soul. His parents receive a type of prophecy from above in order to give the child the name that is fitting for him.

When a person is born and his father and mother give him the name that they have thought of, this is not random or by chance; rather, the Holy One, blessed be He, puts that name, which is necessary for that soul, into [the parents’] mouths. (Rabbi Yitzĥak Luria (Arizal), Sha’ar HaGilgulim, Introduction 23)

A name expresses an object’s spiritual life force, and therefore people are profoundly linked to their names.

An object’s name is linked to its essence:

Whatever something is called in the holy tongue is its true name, the name at the root of its essence. For example, an ox [shor] in the lower [world] is called this due to the root of its life force above, which contains the three letters shin-vav-reish, שו”ר. This is the case with regard to all things…

Even when a child is named after another person, his name fits the root of his soul:

Although we name our children after our ancestors or our relatives, as it says in the Midrash, nevertheless the Ari, may his memory be for life in the World to Come, revealed to us that even those names were not given by chance or by the will of the father and mother. Rather, the Holy One, blessed be He, is the One who places intelligence, wisdom, and knowledge into the heart of the father and mother to give a name that is from the root of the child’s soul.

There is a very strong connection between a person and his name:

Because of this, people are extremely connected to their names. The proof of this is that if a person turns away from all of his other affairs and attends to one thing, and he focuses his eyes, heart, and thoughts on that one thing in total concentration…nevertheless, if someone calls him by name, he will immediately disengage from his business and from his thoughts. All this is for the aforementioned reason, because his name is the root of his soul. (Rabbi Dov Ber of Mezeritch, Or Torah, Bereshit 14)

Further reading: For more on how the first man gave names to all the creatures, see A Concise Guide to the Sages, p. 5.