"I haven't consistently gone by Anakin Skywalker, for one - that was the name given to me at birth, but for a time, I was known only as Darth Vader..."
She describes the naming tradition of the Sith, and how those names were chosen - there's pain in her, deep and old, and she does clarify that she isn't really a Sith anymore, but...
It's context.
The history of the galaxy is long and convoluted, and her mother was a slave taken to Anakin's home world from elsewhere, one among numerous displaced souls - the myths she was raised with were formless, shifting, nameless things, never fully one tradition nor another, growing and twisting with every step in the chain.
She'd - liked the history she learned as a Jedi better, honestly, though she notes it's somewhat strange to take on another person's full name. Their family or clan name, certainly. There's groups she can tell her padawan about, though, if she wants to adopt another collective name.
(She mentions, off handed, briefly, that 'Skywalker' is very likely to become a myth name, sooner or later.)