The brand, called Salt, will be the building society's first subsidiary to use a name other than The Derbyshire.
Salt products will be sold through independent financial advisers. The first will be mortgages aimed at consumers who struggle to borrow from traditional providers.
Salt's brand identity was created by design agency Davison Smiley-Jones.
Press ads will feature the strapline "Salt, making specialist lending simple". Promotional material, online and experiential activity will continue the theme.
The Derbyshire has 52 branches in the Midlands.
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