Yes, your name appears on the Family Tree (although without birth date) because that is the privacy setting currently selected - i.e. “Private” profile that “shows on family tree”.
The only way to remove your name from the Tree and Descendants list is to use the red padlock. The public view of the descendant list would then show you as “private daughter” - as it does for your siblings.
Terminology may not be clear, but choosing the orange padlock that says “Private with Public Tree” is a request to display your name (only) on the Tree for others to see, but without details such as exact DOB, etc.
Hope this helps?