Can you believe that there are so many morons around? I get this stupid information all the time. My dog is a purebred "fill in the blank" and always a cute little name tag to go with it. They then always tell me that, yes, they are so a purebred as they come from a purebred mom and a purebred dad. REALLY.
I refuse to call them by the cute designer name. So, if someone says they have a cockerpoo, I respond "so does your cocker spaniel poodle cross resemble its spaniel parent or it's poodle parent? I then follow up with questions like "does it have the cocker hair coat or the poodle hair coat? is it temperamentally more like a spaniel or a poodle, does it have ears like the poodle or the spaniel and I keep going until they start saying "I don't really know. This is when I hit them with, well you know when you mix breeds like that, you never know what to watch out for for health wise.
BTW, I am not a mixed breed snob. If they tell me they have a cocker mix or a cocker poodle mix, they get the nicer side of me.