I don’t think there was any particular significance to Baxter, unless I’ve forgotten some key discovery? I think people were just amused at SW’s evident taste for surnames as first names — Baxter, Cooper, Raynor etc. I am personally also unreasonably amused by her preference for somewhat exotic, surname-y, androgynous names for their alter egos in both HNTDDD and TSP (Raynor, Moth, Ellias and Baxter) when their actual names are the galumphingly unexotic Sally Ann and Tim.
One of the bits of her first statement that I actually believe (maybe the only one?) is that she dislikes her own name, that Sally Ann made her ‘think of ringlets and gingham dresses’.
What is clearly nonsense (as testified by numerous people telling CH they’d never heard them address one another as anything other than Sally and Tim, even when they’d introduced themselves as Raynor and Moth, and the plaster inscription at Pen y Maes) is that she’d told TW this early in their relationship, and he’d called her Ray ever since, after the ‘family name’ of Raynor she wished she’d been given.
Do we know what she means by ‘family name’ incidentally? Raynor or Rayner is a reasonably common surname. Does she mean it’s a surname that exists somewhere in her family tree? It would have been a pretty unusual decision to give a girl born in 1962 a surname that’s only rarely used as a male first name, especially for parents who’d named their elder child Sue/Susan.
Personally Raynor/Rayner just makes me think of Rayners Lane tube station, which is presumably not what SW was going for…