The name of the baby is Coyotito.
Coyotito plays a vital role in the story. It is his being stung by a scorpion at the very beginning that sets events in motion. His parents, Juana and Kino, need money to pay the doctor to see him.Even although Coyotito begins to heal, Kino becomes fixated on the idea of making money. To this end, he determines to find a valuable pearl which he can sell. Luck at first seems to be with him as he finds the biggest pearl ever seen.
From this point on, Kino becomes obsessed not just with making some extra money, but with gaining enough wealth to wholly transform his family’s situation. He envisions getting married in a church, acquiring all kinds of new possessions, and - perhaps most importantly – getting his son an education.
Kino’s face shone with prophecy. ‘My son will read and open the books, and my son will write and will know writing. And my son will make numbers, and these things will make us free because he will know – he will know and through him we will know.’ (chapter 3)
As can be seen from this quote, Coyotito forms an important part of Kino’s dream. Kino plans for Coyotito to become a great man who will also free his parents from ignorance and want. It is for Coyotito's sake most of all that Kino pursues his dreams of wealth.
However, it all goes horribly wrong. Kino runs into all kinds of difficulties when trying to sell the pearl, the family incur many enemies, which ends with Kino killing a man in self-defence and being forced to flee along with his wife and son. This is a prelude to the final tragedy, in which again Coyotito features prominently, as he is shot and killed by one of the men who are tracking them down.
Coyotito’s death spells the grim end of Kino and Juana’s initial high hopes and dreams in finding the great pearl. They return home having lost everything, and cast the pearl, which has brought them so much misfortune, back into the sea.
The baby in the book name is Coyotito.