Don't let other people bother you at all! As long as you know what Emma and Milli are, that's all that counts.
There will always be some people that want to try to put you down, don't let it get to you at all. You were very courteous and polite, don't feel bad you didn't say anything mean to her. Next time maybe you should just tell someone like that to do some research on Yorkies on the Internet, as there are Yorkies of all sizes, shapes, and colors!