It struck me as a hint as well, but I don't think it was specifically saying Voldemort's name that did it. It's just that she openly states that she believes him to be alive and active, and thus reveals to a surreptitious listener that she--and likely Dumbledore--have this knowledge or are acting under these beliefs. That's more than enough, given the interest that the murderer and Quirrell (if they are different people) would have in the room at the time.