The couple is expecting their first child in July. The baby's gender has not been disclosed.
West has been telling friends he likes the way North sounds with his surname and he has ranked it high on his list of possible baby names, The Sun said.
The name would be a surprise move since Kardashian's mom's name is Kris and she has given all her children names that begin with K.
Celebrity Families of 2014 [PHOTOS]
Tatiana Maslany to make her New York stage debut