Hi Dharik, welcome to Streamlit! 
For this use case we recently had a session state update which can help save the username when logged in.
To see an example of when I myself had this question you could look through this post:
To learn more about Session state and usage of it you can check this out:
It will probably be something in the form of:
if "username" not in st.session_state:
st.session_state.username = "the username you want to save"
now you can retrieve it with st.session_state.username
have a great day!