The recent drama High Society caught my attention. Im just wondering if you guys could recommend me something that fits that description that has finished airing or about to. 

Mmh, you can try Couple or trouble. It's also about a rich girl, she doesn't really act humble (in fact at the beginning she's very arrogant) but then she's forced by the events to become poor and live in a shabby environment and thus change her attitude. And her identity is also hidden. ^^ 
Horse Doctor
Ugly Alert

They're both lengthy, but they do have strong female characters who hide their true identities as chaebol/noble.
Thank you for the recommendations.

Could you guys recommend something that  is shorter than horse doctor / ugle alert hehe.. those are over 100 episodes...
And about couple or trouble , i wanted something along the line of humble / kind person deep down and isnt forced to actually live poorly but volunteers to do so.

If you guys have watched " Me too, Flower ", something along those line but the rich and powerful but humble person is a female/ girl. 
Ad Genius Lee Tae Baek has what you're looking for, but I didn't want to recommend a drama  I didn't like. If you're looking for a lot of romance with a bunch of kisses, this drama isn't for you. I still recommend the first two I named, not only because they fit your criteria, but both are good dramas.

Ugly alert

There are too many episodes in the drama but don't be disheartened you will love the drama it too good

Ugly alert. As mentioned about it is super long but super worth it.

Others:

  • Lovers in prague - daughter of the president and is a diplomat (works for the embassy)
  • Khun chai pawornruj - heiress who hid her identity while travelling
  • Tarm Ruk Keun Jai - kind heiress in search for her biological dad and seeks a job at a farm

It's a Cdrama, but Accidentally in Love is exactly what you're describing