After obtaining the Red Jeweled Brooch, you can do one of four things with the Young Yharnam Girl:
- Give her the brooch.
- Withhold the brooch and instruct her to go to Oedon Chapel.
- Withhold the brooch and instruct her to go to Iosefka's Clinic.
- Do not tell her anything or do not talk to her again.
Keeping the brooch and using it nets a bloodgem that grants physical ATK UP + 2.7% and a boost to rally potential by 1.8%.
The short-consequences are as follows:
She will be distraught and leave the next time you load the zone.
She will be thankful for the safe place and leave. You keep the brooch.
The same as (2).
She will eventually leave on her own. You keep the brooch.
The long-term consequences may surprise you:
Killing the pig in Yharnam's sewers (under the bridge outside Father Gascoigne) will yield a Red Messenger Ribbon. After the moon turns red, her sister will be found in the window. If you show her the ribbon, she will eventually leave and you will find a White Messenger Ribbon under the ledge near the window.
The same as (1).
Iosefka will thank you and give you a Lead Elixir. Later, you can gain access to the back of Isoefka's Clinic and you will find the girl. She will a Formless Oedon rune.
Nothing further happens. Her quest line ends when night falls.