Reality TV star Kim confirmed the name on her website, three days after announcing that he had been born.
The couple's daughter, who is called North West, was born in June 2013.
Kim announced that she was pregnant for a second time in an episode of Keeping Up with the Kardashians at the end of May.
The couple haven't said anything about why the name was chosen but some reports suggest it's "because she had such a difficult pregnancy".
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