Cowell's followers have posted many suggestions, including basic dog names such as "Lily and Coco" to humorous names like "Paula and Randy" -- referencing his fellow former American Idol judges Paula Abdul and Randy Jackson.
Cowell first announced his plans to adopt two dogs in early September.
"I am going to get two dogs when I get back. Probably cairn terriers. If any rescue shelters have some who need a home let me know," he tweeted at the time.
Cowell is currently dating Lauren Silverman, who is pregnant with his first child. It's been widely reported the couple is expecting a baby boy, but both parties have still refused to publicly disclose the gender.
"Let's put it this way, I wouldn't expect her to be a single mother," Cowell told Seacrest.
Silverman, a 36-year-old New York socialite who's expecting Cowell's baby this winter, was still with ex-husband Andrew Silverman when news of the pregnancy first surfaced in July.
The "adulterous affair" allegedly ended the couple's marriage and led Andrew, Cowell's former close friend, to file for divorce on July 15 -- citing adultery and naming Cowell a co-respondent. Lauren and Andrew have since reached a divorce settlement out of court.
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