The Spanish club, who are based in the outskirts of Madrid, earned promotion to La Liga last season for the first time in their 88-year history.
As it stands, the club are officially known as Club Deportivo Leganes, but Moreno wants to become 'Leganes Madrid' in a bid to help attract sponsors and develop the brand away from the pitch.
"We want to have our name put on the map of the world so rather than being Leganes CD we would want to be Leganes Madrid," Moreno told Sport 360. "We are in Madrid, in a suburb of Madrid and we want this to happen - it's about exposing the club to the outside world.
"I don't think we could ever change the name of Estadio Butarque. The whole city is named after Butarque and the fans would not like it. But the name of the club, it is just a minor adjustment that could make a big difference."
Last month, Leganes, who currently sit 13th in La Liga, agreed a deal for Saudi Arabian company MBUZZ to appear on the club's shirts.