@gingejbee
//Hypo...of course you don't have to give them your mother's REAL maiden name, do you?//
i) I hadn't thought of that.
ii) I'm not one for imaginativeness when put 'on the spot'. Any pause and they'd know you were lying.
iii) I'm forgetful so, when challenged, I'd give them all I could remember (the real name) and I'd be locked out.
@atalanta
//It's not as if this person is denying his/her age; just being shy about the date, probably to try to save us all any expense.//
Shy, possibly an introvert. Nothing more excrutiating for them than a crowd sneaking up on them at their desk, even if it turns out to be a nice surprise.
You asked, politely, when their exact birthday is and they declined to say. Why not leave it at that?