Why had Portgas D. Ace refused to take his father's surname?

Question

Why did Portgas D. Ace refuse to take the Monkey D. name?

What had his father done to him to resent him that much?

Answer 1

First off, his father is Gol D. Roger so his birth name was originally Gol D. Ace. However, he did get adopted by Monkey D. Garp. And before his execution, many assumed that he's Monkey D. Dragon's son.

Moving on to your question as to why he rather chose his mother's name that his father's was that he felt grateful for her mother's willpower and sacrifice just of keeping him in her belly for one year and a few months after just to save him from the Marines of finding out he's Roger's son.

"Just before passing away, Rouge gave him the name Gol D. Ace. However, Ace, grateful to his mother for her sacrifice, chose to take her name instead." (taken from Wikia)

For your second question, it also has been revealed in the manga that he did not resent Roger that much in fact from the flashbacks, Ace would get violent to anyone who would speak ill of his father. Let's just say Ace was indifferent to the idea of Roger being his father. Because after all, Roger was already dead wen he was born.

Of course, for proof you could check out the wikia page of Ace.