This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
Note that the 名 portion is the alternate reading, so adjust your thinking accordingly so you can get to みょう. Just imagine someone saying "more" with a funny accent. They say "myou" instead of "more". Imagine them saying they have myou people in their family than yours. Their surname is spread amongst myou people than yours.
What is Sakura’s last name?
If you tell me Koichi's surname, I will give you a figure of Tetsujin 28 in return.
I will never tell you my family name.