I noticed that the reference to the Baronetage book referred to "all the Marys and Elizabeths" who had married into the Elliot family. It seems that Anne was 'nobody' to Sir Walter from birth, not even being worth one of the illustrious family names.

He probably would not have minded that his first child was a girl, and was happy to give her a treasured family name (or name her after her mother), but no doubt Sir Walter would have wished and expected Anne to be a boy--an heir--another little Walter.