Yes, you must change your name to be called after a general name such as: daughter of Abdullah.

I was adopted by a Christian family in America where I am from. Per the tradition I was named by the family. Alhamdu’liEllah I am a revert to Islam and understand that it is not permitted for me to have my adopted parents surname, however, I have no idea who my biological father is. Should I address this issue and change my name, if so to what? Please advise.