Yes, the name’s were set. Actually the whole characters are set. The author specifically said that “they are her characters, not yours” though she probably said it in a nicer way. Sexual orientation was never explained in that game though. It was still far too early in the WiP stages (and still probably is). One of the characters was more shy around girls, you can take that how you will. The only choices you could choose were the actions they took and how they responded to some situations. However, I thought all three characters were amazing, I enjoyed playing as “them”. I did not enjoy the MC in this story.
Choices, yes. Customization, no. It is called “Choice” of Games. Customization is optional.
EDIT:
I found it! Yes!
Hey @poison_mara you’re in here too.