Wastholm.com

Before a green-rumped parrotlet is even able to chirp and squawk, mom and dad teach it a distinct series of sounds used by parrots to recognize a specific individual. In short, they give their nestling a name.

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Among other animals known to imitate the sounds of others and give each other unique names are dolphins and humans (and, possibly, whales.) Like humans and dolphins, parrots are highly social. Using names makes it easier to keep track of relationships and individuals.