Complementary events are the events which are opposite of the given event.
For example, for a "rainy day", its complimentary event is "not a rainy day".
We can also say, If A is a given event, then " not A" is its complimentary event.
In the given question we have been given the event of choosing a girl's name when drawing names from a cup in class.
Now in class as there can be boys or girls, the complimentary even of choosing a girl's name is choosing a boy's name.
Option C) is the right answer.