The name, which is Hebrew, means song.
The connotations to the Bible a strong, especially since many would be familiar with the Book of Psalm.
E! News has been told that Psalm "was chosen by Kanye and is a representation of their spirituality."
"It was a very important to him, and Kim wanted the name to have a significance that held a true representation of their family, so she agreed on the name."
A second source also spoke of the unique name.
"The name Psalm was very important to Kanye and where he is spiritually," they said.
"He presented it to Kim and she thought about it and ultimately agreed."
"Kanye felt very strongly about it and Kim thought the way he explained it and the meaning behind it was beautiful. Each name they have chosen has a special significance."
The name Psalm just "felt right."
Baby Psalm joins Kim and Kanye's daughters Chicago, 15 months, and North, 5, plus son Saint, 3.
The 38-year-old announced the birth of her son via surrogate, tweeting, “Here’s here and he’s perfect!”