Lion's Fake Daughter

What happens when you are isekaied into a world that can go on without you and you are told how to get back but is stopped by the world's male protagonist? Now you end up trying to pretend to be someone you're not but isn't given enough information on how to pretend as that person.

A woman from modern times faints from overworking and wakes up as a kid who never existed in the manga.

Somehow she is confused with the actual female protagonist and now she is forced to live as the Duke's daughter, Leonia Boleoti.

It's a dream for everyone else but it's a nightmare for her.

"I'm not Leonia! I can never be her!"

"You are my daughter and I named you Leonia."

"Duke I'll find your daughter and escape to my world!"

"They say children have wild imaginations."

"She's real! I know because..." She is the main character in a fantasy manhwa I enjoyed.

"I read that children often imagine an invisible friend because they're lonely. If my daughter is so lonely, I should send her to play with the other kids."

"Why are you never taking me seriously!"

She did the one thing no female lead in anime did upon meeting the protagonist.

She told him of her reincarnation. He listened earnestly but he didn't take her seriously!

He still says that she is his daughter and takes her to the Boleoti mansion, her new (forced) home.

It doesn't help that everyone around her becomes infatuated with her and her confusion.