1. What do you think is the toughest race in sports?
2. What do you think the toughest race is in sports?
3. What do you think is her name?
4. What do you think her name is?
Which are grammatical among them?
All are grammatically correct, but numbers 1 and 4 are more commonly used.
I'm not a teacher of English, but I have spoken it for (almost) all of my life....