I would get different reactions. Everything from surprise to unbelief to an awkward silence of them trying to figure out what to say (Usually they end up saying something like, "oh" and "is that a family name?" or "is your father a dentist?" All the honest people would say right out "that's a weird name"). What do you say when someone says their name is Flossie? Afterwards I would say just kidding and laugh a bit.
One time my companion and I were talking with a group of elders about first names. When they asked me what my first name was I of course told them Flossie. The reaction was nothing. Straight faces all around. So, I left it at that. Three weeks later we were talking again about names and I decided to tell them that I had lied to them. Turns out that when I told them my name was Flossie as soon as I was out of earshot they had laughed and amongst themselves they would always refer to me as Sister Flossie. It became a joke and most of them called me Flossie to my face after that.
I really don't get much opportunity to say my name is Flossie anymore unless it is at Jamba Juice, and they always spell it wrong! Can you imagine spelling it Flossy instead. It's criminal. Flossie is insulted by the mere thought of it.
Oh, and Flossie hates the dentist joke.
And yes, she flosses every day.