Ugly Duckling Series: Perfect Match** - she hides her wealthy background
The K2 - she tries to run away / her existence is hidden from the world
K-POP - The Ultimate Audition - the FL leaves her classical music training without her parents' knowledge to try and become a hip hop idol; she joins a talent agency where her uncle is the CEO but no one is aware of their connection
Princess Wei Young* - hides her true identity (although she's still a high-ranking noble)
Princess Agents* - she's not aware of her own identity (and they never really resolve it)
Eternal Love / TMoPB* - there's a period where the FL is not aware of her true identity
Healer - she can't remember her birth parents / is not aware of her mother's circumstances
The Master's Sun - not one of the leads (the ML's deceased ex-girlfriend was an orphan, adopted by rich parents in the UK, who pretended to be her penniless twin sister who was raised in a Korean orphanage)