To be clear, as you were not the legally recognized father the mother didn't "take" the child as you allege. As you were not the legal father the daughter's last name was not illegally changed.
Nothing can be done about it, really. As your daughter is now in her teens I suspect that she'll have something to say about you trying to unilaterally change her name. How you try something novel. Be a good father. Ignore the mother's baggage and establish a decent relationship on your daughter's own merits. Believe me, with a teenager this will already be difficult enough. If you choose to blather on and on about mom then you will alienate your daughter and you'll discover how fun that is.

