She might have some trouble getting mileage credit; no other likely
consequence. I was once issued a BP under the name Chad Stockov
and (under similar circumstances) boarded without looking at anything
but the seat number. Turns out that a bunch of BPs had been issued
at once and I'd just been handed the wrong one. In this case, someone
else sat in my seat and could see my mileage plan number (big whoop),
but of course I got credit for the flight.