Oscar Wilde's comedy of manners, which punned on the name Ernest and the virtue of earnestness (the play was titled The Importance of Being Earnest), attempts in part to explore the significance of a man's name. Indeed, Anne has asked, does a name matter?
One can't explore this without passing through the Bible ("Thou shalt not take the name of the Lord thy God in vain," Deut. 5:11) to Shakespeare ("What's in a name? That which we call a rose, By any other name would smell as sweet," Romeo and Juliet, Act 2 scene 2).
What's in a name? A lot. The right to bestow a name is an archetypal symbolic expression of seniority and power.
The biblical text has God according to Adam the right to name all the animals, which in the ancient world meant having power over the thing or being named. American Indians similarly spoke of naming evil spirits as a way of dissipating their power.
What you call something is still so powerful that the government routinely resorts to euphemisms for events the public might find distasteful. The name given to the victim of murder or mayhem in war is a "casualty," which sounds almost as if all that has happened is something no more serious than stubbing one's toe in a darkened bedroom.
As for Shakespeare, he wasn't arguing that names were irrelevant, but that love could overcome the chasm between someone named Montague and another named Capulet. Yet the names stood for an intense rivalry between competing clans.
The names we give ourselves and others are telling and influential. For example, the Chinese word for "Russia" means "land of hungry people," whereas the word for America means "beautiful country."
In the USA we don't call Italians and Greeks "Mediterraneans," but we call Japanese and Koreans "Asian," and Salvadorans and Chileans "Hispanic." Clearly, there's a matter of point of view. In the prevailing view, Europeans are distinguishable from one another, whereas non-Europeans come in continental globs. Moreover, forebears of Americans of European origin were all "immigrants," whereas non-Europeans are commonly called "aliens."
Who will argue that there is no difference between calling someone "Nigger" and "African-American"?
As to the word used to name the deity, there are entire volumes written about the Hebrew variants, with elaborate explanations of the meanings, ranging from the one who is to various attributions of might.
In English, the word is not devoid of meaning, either. "God" comes from the proto-Germanic "guthan" (in German, Gott), from the proto-Indo-European "ghut," meaning "that which is invoked." In Sanskrit, huta, meaning "invoked," was a nickname of the god Indra, the god of weather and war. Some trace it instead to "gheu," which means "to pour, pour a libation."
"Deus," the base in languages of Latin origin for Dieu, Deus, Dios, Dio (French, Portuguese, Spanish and Italian, respectively), the Greek genitive form of Zeus, the chief god from Mount Olympus. Zeus, for its part, traces back to the Sanskrit "deva pitar," meaning "father god." The root meaning of all these words is related to the word for "day," originally a reference to a bright, clear sky.
The biblical prohibition against the use of the deity's name was intended to prohibit human dominion over the deity, against the tendency of religious folk, then and now, to think they've got God in their pockets.
For my money, names and naming are hugely important.