The Missing Snowflakes

fake princess identity
Fl is also a doctor
the end is a little bit similar
ML personality is similar

Both are historical mini dramas in which the FL is an identical twin, and due to it being illegal and punishable by death, has been hidden her own life. When her sister dies or is presumed dead, she is forced to pose as her and marry the ML.

Both are historical dramas in which the FL is an unfavored identical twin who ends up swapping identities with her dead sister and marrying the ML.