Hinagiku suddenly started calling Hayate by the first name after the marathon race..what was the reason exactly?
Do you mean on why she called him by his family name ("Ayasaki-kun") after the marathon?
If so then, she called him that because she was still mad at him after he had lured her on a suspension bridge during the Hakuo marathon and had also used her fear of heights to end their confrontation.
To expand on Hina sama's explanation, calling someone by their family name is a polite way of refering to someone in contrast to being "close" or "intimate" friends (whereas they call them by their surname.) Usually you would call someone by their family name when you don't really care much for that person or is someone you don't know as to show respect. Kind of like calling your friend's parents Mr. <lastname> and Mrs. <lastname> instead of their first names.
And the reason why Hinagiku was doing that was as Hina sama stated (kind of saying we are "not friends" in a way I guess.)
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well ...I thought hayate will apologize to her though it was for her mistress...Still it is not fair use someone's fear so wrongly...I don't blame hina..