Posing with two-week-old Miley Beau Pearson for Hello!, Sam said the name had nothing to do with her famous namesake, adding: "I just really like the name."
The 37-year-old said the success of winning the ITV singing show meant she could afford to have a third child along with nine-year-old daughter Brooke and five-year-old Tommy.
The former prison officer said: "I always wanted three kids, but before The X Factor we couldn't afford it. So I was resigned to the fact I would just have the two.
"Then next thing you know I find out I'm pregnant and I was like, 'Yes. I'm finally going to get my wish."'
And her daughter already has one celebrity connection - godmother Sharon Osbourne.
Sam said: "Never in a million years did I imagine I'd be having a baby whose godmother is Sharon Osbourne".
She also revealed she nearly went into a very early labour at one stage, saying: "I got told at 29 weeks that I had a 70282Slideshow-164878%