The 35-year-old gave birth to the baby, her third with 31-year-old Scott Disick, on 14 December. He will share a birthday with big brother Mason, who turned five that day.
Taking to Instagram at the weekend, Kourtney shared a cute snap of her holding the baby's hand. She wrote: "Madly in love with my little Reign Aston Disick."
According to sources, the couple struggled to agree on little Reign's name, with Scott wanting it to be personal to them.
An insider told a US website: "They both fought over the name, and Scott wanted to stick to honouring their fathers, but Kourtney got more adamant that it will be unique."
Kourtney and Scott are also parents to two-year-old daughter Penelope.
The reality TV star recently admitted she feels her best when pregnant, believing her body was made to have babies.
She told DuJour: "I really feel so comfortable, and almost at my best, when I'm pregnant.
"I don't know, I just feel like it's such an amazing feeling, the transformation that your body goes through and knowing that this is what my body is made to do, there's just something that's so empowering and beautiful and I just really embrace it."