Why were Branwell and Charlotte Brontë obsessed with the name "Caroline"?
It appears in Branwell's poetry, and as a heroine in Charlotte's Shirley (1849).
Could it be due to Lady Caroline Lamb's influence on Lord Byron and the Byronic hero?
Charlotte Brontë quoted Lord Byron's The Corsair (1814) in Jane Eyre (1847), and Branwell Brontë quoted Lord Byron's Don Juan (1819-1824) in his 1847 letters.
The influence of Lady Caroline Lamb on British society was huge.
Another potential source of Caroline was Caroline Bingley, the creation of Jane Austen in Pride and Prejudice (1813).
Charlotte read Jane Austen throughout her life.