Mmmhmh I can say various things though I don't know what you wanna know but I guess with the basics : 
The imae does get a name, and is named by the 2nd male lead (so not garon) I think he names him Roha if I remember well it means smth like I hope someone with purple eyes live well in chapter 39 I guess...maybe it's 38... srryyy
buuuutt garon does give him a name later, even though it's not in the imae's eyes (and yes his eyes become red... 😥) (btw Garon gets very angry that the imae got a name and want to pluck his eyes out but doesn't do it cause it's a sign of him changing) he names him  Damha which means “a faint, purplish sunset.” And later on, when he becomes a painter he uses the name for his pen 🥹
and I think the obvious question : yes they fall in love and ends up together. Don't remember very well but I think it's a good thing, Garon needed someone to shows him compassion and all this stuff 
Also small stuff : Garon admit not remembering he killed the imae's mother but he goes to the Imae's village every 7th of the month I guess to go and clean and grave ect....he confesses it in the last chapter and that's a very touching scene cause iykyk
Don't hesitate to ask more if you want :) tried to put the basic but I may have forgotten things you wanted to know ! 

of course : they get their happy ending !