Since I don't know the exact 'the quiet girl story', it's hard to say. But surely there would be the quiet girl herself. There might also be her family members, like her parents or siblings who play important roles in her life.
The main characters are Sean Thornton and Mary Kate Danaher. Sean is the American - Irish man who has returned to Ireland. Mary Kate is the Irish woman with whom Sean falls in love.
The Quiet American himself is an important character. He is likely a young American with certain ideals and a sense of mission, but his actions have complex and often negative impacts.
Since it's called 'the quiet man novel', the quiet man is surely one of the main characters. There could be other characters around him, perhaps his neighbors in the place where he lives. Maybe there is a character who is his opposite, very talkative or outgoing, and their interactions form an important part of the story. Another possibility is that there is a family member, like an older relative, who has some influence on the quiet man's life.
The Abbott family is among the main characters. They are trying their best to survive in this dangerous world full of sound - sensitive creatures. Each family member has their own role to play in the family's struggle for survival.
The main characters are Thomas Fowler, a British journalist. He is cynical and has a complex relationship with Vietnam. Then there is Alden Pyle, the 'quiet American'. He is an idealistic young American who gets involved in Vietnam's affairs with his own ideas of how to 'help' the country. And there is Phuong, a Vietnamese woman who is caught between Fowler and Pyle in a love triangle.
Not having more details about this story makes it difficult to name the main characters precisely. However, if it's a typical story, aside from the quiet woman, there could be a love interest. Maybe a man who is intrigued by her quiet nature and tries to get to know her better. There could also be a nosy neighbor or a confidant that the woman shares her thoughts with, even if it's not through words but through some other form of communication.
There's Thomas Fowler who has seen a lot in his journalistic career and has his own moral ambiguities. Alden Pyle, who is the titular Quiet American, with his clean - cut American image and his dangerous, if well - intentioned, plans. And Phuong, the Vietnamese woman, whose life is caught between these two very different men and their worlds.