I can't remember the name of a particular manga (although it might actually be Korean or Chinese; I don't remember).

The MC is in love with a rich girl who has the same name as him, some weird guy grabs him and says to come with him because he's the hero and is needed in their world to defeat the demons or monsters or something. He runs away, but ends up being killed trying to protect the girl from a dragon that I guess came out of that fantasy world. He wakes up and he's in the girl's body.

Other details: the girl has a fiancee and he's a total douche, but she has no say over her life because I think she was adopted or something?
Also the guy I think turns back at some point and visits his dad and then gets stabbed or shot or something, but somehow magically heals.

I can't for the life of me remember the name or find it, and it's killing me. If anyone could give me any pointers, I'd be much obliged.

I'm having a hunch that it's the webtoon "Hero is a girl" by PXS_STUDIO
http://www.webtoons.com/en/challenge/hero-is-a-girl/list?title_no=12859

Yes, that was it! Thank you!