Currently airing: 

Here we meet again (2023 - China) - Why I recommend it: We only have 6 episodes aired, but the FL is rich (her grandad is like the owner/ceo of enterprises) and she's on a mission at one the branches, so her grandad forbade her to tell anyone about it, so people think she's poor.

Completed:
Eccentric! Chef Moon (2020 - S. Korea) - Why I recommend it: the FL is famous designer, but she temporarily loses her memories and everyone thinks she's poor.

Hak Lai, My Lady (2023, Thailand) - Why  I recommend it: The FL has a rich family / a heir, and while on the run to look for her long lost father, she has to pretend to be poor and work in a farm.

Occupied heart (2018, Thailand) - Why  I recommend it: the FL is an actress (rich) and after someone tries to kill her, she is lost in an island with her son, and since she has no idea about who is trying to hurt her, she pretends (for a little bit) to be poor and lost. 

Please, feel at ease Mr, Ling (2021, China) - Why  I recommend it: the FL has problems with her rich family, so she doesn't rely on them, and everyone thinks she's poor and struggling. 

Snowdrop (2021, S. Korea) - Why  I recommend it: During South Korea's dictatorshiph, the FL is secretly the daughter of the ANSP Director (important and rich), and no one from her college knows it until she has to tell the truth since North Korea's spies kidnaps the college and its students/staff.

The Crown Princess (2018, Thailand) - Why  I recommend it: The FL is a princess, the heir to the throne, and for security reasons, she has to pretend to be the ML's wife, a simple lieutenant from Thailand.

Who Rules the World (2022, China) - Why  I recommend it: The FL is a famous martial artist, but in reality, she's a princess and no one actually knows about it.