It looks like the only source to suggest Frances Mary is Mary Ann Short is the 1854 marriage to Charles Hamilton Broadwood. Even the 1861 census has her down as another name, Mary Louisa. She had gone by several different names, including Louisa Beresford, as noted on a newspaper clipping from The Times in 1865.
It's likely she could've changed her name to Frances at some point too.
Bethany