It was revealed on Wednesday (November 9) by music charity Rhythmix that Simco - one of the companies which Cowell owns - was still seeking to trademark the name.
The charity - which works with vulnerable young people - had written an open letter to Cowell pointing out that although a girl group on The X Factor had already changed their name from Rhythmix to Little Mix, the application to trademark the name still appeared to be active.
A spokesperson for Syco told The Guardian that the company is "happy to withdraw the application for the trademark", stating that the original offer was made at the same time that the group's name was changed to Little Mix.
A statement on the charity's Facebook page read: "We are pleased to report that apparently Simco have formally withdrawn their trademark application in response to the public pressure you all brought to bear today.
"I am afraid we are unable to officially confirm this as we have still not received any direct communications or contact from Simco - we get our news from the national press like the rest of you!"
The charity said that it believes the news will be officially confirmed later on Thursday, adding: "We look forward to this official confirmation being accompanied by Simco's final proposals to ensure that the legal costs do not fall on the charity... In the meantime, once again, thank you."