The X Factor boss, who is well-known for his ego, took a part-share in the animal with the Geordie duo last month.
The presenters said they hoped the horse will run its first race during the next few months, during an interview for tonight's Jonathan Ross Show on ITV.
Declan Donnelly said: "We had to name the horse because obviously it wasn't named for racing, so we had a chat with Simon. His first suggestion was 'I think we should call him Simon'."
They eventually settled on the name It's A Yes From Me – a reference to a phrase often used by panelists on Cowell's talent shows.
Ant McPartlin added: "It hopefully might run in the summer."
Ant and Dec previously owned another horse, which they recently sold.
They also told Ross they have had to insure themselves as a double act, so the other would get a payout if their partnership was jeopardised.
Donnelly said: "Financially the other one would get a kickback off that. Every cloud – we have insured each other against that."
McPartlin went on: "The problem with that is that if one of us has a fatal accident, we're the first one that the police will come to because we've got a motive."
The pair famously had a chart career under the guise of PJ and Duncan, a spin-off from their roles in BBC series Byker Grove. But McPartlin said of their songs: "I can't even name them. They're all pretty bad."