Question:
Is it permitted for a girl to put a picture of herself as her profile picture so that if others text her they will see it?
Answer:
From a strict halachic perspective I don’t see why it would be forbidden, however it is more refined and tznius for a girl not have her picture on display for everyone to see. For friends and family, it is alright, but when you are sending a text to total stranger, you most probably don’t want them seeing your picture.