It’s all in the wording.
‘Cath Kidston Fabric Bag’ makes it sound like a fabric bag made by Cath Kidston.
‘Bag made with Cath Kidston fabric’ tell you exactly what it is, a bag made with CK fabric.
Personally I would be using the second option - if there is anything in the wording that implies the item is made by the brand name then it’s best steered clear of.