Perhaps its gender-bending could be explained by
Bryn Mawr, which is I think a women's college. Wouldn't ambitious parents give their daughter a name associated with high-flying exclusivity? And when she became famous as an actress, other parents might perhaps find both associations working for them.
Also, a single-syllable female name ending in -n is pretty familiar:
Ann,
Lynn,
Jean and
Jane and
Jen,
Gwen ... so Bryn(n) could fit the pattern.