The 'Call My Name' hitmaker - who has two-year-old Bear with former partner Liam Payne - refused to be parted from her baby while they were still in hospital after he was born because she was convinced she'd be given the wrong child back.
She said: "When I had him, first of all I wouldn't let the doctors take him out of the room. I read this story about two girls being swapped at birth and it was playing on my mind. I was so irrational...I didn't want anyone to take him."
The 36-year-old star explained how her son's unusual moniker came from a nickname he was given while they were in hospital as she'd initially struggled to come up with a unique name.
Speaking on Ru Paul and Michelle Visage's podcast 'What's The Tee', she said: "When I was in the hospital, he used to make these noises. We had specialists coming in to see what was going on, he was breathing like - quite cute but nothing worrisome.
"It was just him. The midwife used to come in and say: 'How's the little bear?' I didn't have the name prior...
"I couldn't get the nickname out of my mind. We toyed with others but I didn't want him to be the third and such and such in his class. I wanted him to have a unique name."
Cheryl's own name has drawn some attention over the years, having ditched her surname Tweedy for those of her husbands, Ashley Cole and Jean-Bernard Fernandez-Versini, and she admitted it was a "tricky" thing to navigate.
Asked if she regretted changing her stage name for her married names, she admitted: "'Yes I do. But it's a difficult one isn't it? 'I was Cheryl Tweedy, and then I got married and was married for six years to him.
"Then we broke up and it was my name by then, everybody knew me by then.
"And then you meet somebody else, then people are addressing you by your previous husband's name, it's a tricky one."
Ru then joked he couldn't pronounce her second married name and his guest quipped: "You don't have to, you can forget all about that. We don't worry about that."