Programme bosses apparently want Lloyd to adopt an "edgier" one-word moniker but cannot use Lloyd's first name because it is already taken by the famous 'Shoop Shoop Song' singer.
However, Cole had to step in when it was suggested that Lloyd attach the first letter of her surname to make 'Cher-L', according to The Sun.
A source said: "Cher has already been called a mini-Cheryl and now she could end up with almost the same name.
"X Factor chiefs want Cher to change her name after the show to give her something a bit edgier and more fitting to her image. They don't like her having two names and think she should have something a bit different.
"She can't be known as Cher so the idea of Cher-L came up - but her mentor didn't like it as it was so similar to her own name. Cher loves Cheryl and values her input and ideas but it doesn't look like she'll get her way on this one."
Bookmakers recently slashed the odds of Lloyd winning this series of the ITV singing competition after her celebrated performance of Shakespeare's Sister's 'Stay' on Saturday's live show.
> Cher Lloyd explains 'Stay' tears