I also have a step-daughter who is almost 12 years old and I did look into this at one time. We changed her name by deed poll which is easy enough to do and also inexpensive, but deed poll is not recognised in the Philippines and now that she has British citizenship and a British passport in her new name, we find that we are unable to to apply for dual Filipino/British citizenship for her and unless we go through a full adoption process in the Philippines, she will lose her Filipino citizenship completely.
At only 12 years old I don't suppose this matters much, but who knows what the future holds, she may one day want to live, work and own land in the Philippines which she will be unable to do as things stand at the moment. Unfortunately it would be very difficult to go through the adoption procedure in Phils when your living in the UK and when it comes to the cost, because your from the UK the attorneys out there seem to just think of ludicrous figure and then double it.