碧茜 transliterates English 'Betsy/Bessie/Becky':
碧 (bì, 'jade green') approximates the 'Be-' onset and
茜 takes its phonetic loan reading xī (used specifically in foreign-name transliteration; the everyday reading of
茜 is qiàn, 'madder red'). Together they form a name that reads 'Bìxī' — close enough to 'Betsy/Bessie' and visually pretty (jade + madder).