Cowell told Seymour, "My number one choice is Simon because I like the name." His second choice would be Eric, after his father. "His birthday is going to be very close to my dad's birthday," adding that his father would be very proud and amazed if he were here.

The "X Factor" judge said he wants to adopt the same parenting style with which he was raised. "Be cool about it, and don't worry about things to much� the way my brother and I were brought up, it was kind of relaxed. There were no self-help books."

Simon is also looking forward to having his son follow in his footsteps. "I really would like the idea of teaching him how to run the business."

As for "X Factor" this season, Cowell predicts Alex and Sierra could win it all, and he hints at some of the big names that might perform on the show, like former judge Britney Spears. "I'm in touch with her manager all the time, so maybe it'll happen, yeah."