The 'X Factor' star - who has three-year-old Eric with girlfriend Lauren Silverman - made a last minute decision to honour his late father, also Eric, with his firstborn but even now he'd still give serious consideration to changing the tot's moniker again.
He said: "Do you know Eric was going to be called Simon? I was going to right until the end then someone said you just can't do it. I was quite happy.
"In fact, I said to him the other day, 'Your name was supposed to be Simon. Do you prefer Simon or Eric?' He went, 'Simon.'
"Maybe I'll change my mind."
Though the 58-year-old music mogul never planned to have children, he adores Eric and would consider having another baby in future.
Asked about the possibility of having more kids, he admitted to The Sun newspaper: "I didn't plan any in the first place but I'm glad it happened so, you know, I don't rule anything out."
And Simon never expected to love Eric as much as he does.
In a joint interview with Cheryl Tweedy - who has seven-month-old Bear with boyfriend Liam Payne - during a break from filming their 'X Factor' Judges' Houses segment together, he said: "I said to Cheryl on the plane, you don't realise you can love somebody as much as you love your family, your parents... And when it happens it is amazing."
Simon recently admitted he turns to his late parents, Eric - who passed away in 1999 - and Julie, who died two years ago, when he needs advice on "difficult" situations.
He said: "I still talk to my mum and my dad in my mind now if I am having a difficult decision or I am struggling with something.
"I have a mental conversation with the both of them and I absolutely know what the answer is - it is the weirdest thing."
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