In Amaranto, is Troy a girl or boy?
This is Troy's profile from the official site's character introduction.

Although Troy's appearance is like a boy, Troy is a she. From the last paragraph of Troy's description:

口数が少なく、常に行動を共にする双子も
彼女のことはよく知らない。
Does not talk much, and even the twins whom Troy usually act together with
do not know much about her.

While VNDB claims that she is also a transgender, I don't have any proof to support or counter it. However, from the sample dialog on the image,

「そんなの、ボクには関係ない。
　　君たちの好きにすればいいだろ」

she refers to herself as ボク (boku) which defines her personality as a bokukko (Warning: TV Tropes link)

A Bokukko is, literally, a girl who uses the first-person Japanese Pronoun boku, primarily used by boys and young men. [...]
Most bokukko are tomboys, but not all; sometimes it just indicates that the user is a Plucky Girl or unaware of social norms. [...] Although none of this has to be reflected in her appearance, bokukko are usually either flat-chested or extremely well-endowed.
This speech pattern can also be used to keep a character's gender obscured—is she a boyish girl, or a girlish boy?

Last but not least, Kisaki Kotori ― the voice-actor herself ― listed her role on her official site as female for Troy.

トロイア役 (Troy)　♀


Regarding the name トロイア (toroia) as Troy, most possibly it refers to Troy, a city used as the setting of the famous Trojan War. Japanese Wikipedia lists トロイア (toroia), トロイ (toroi) and トロイアー (toroia-) as the possible pronunciations.