Change my daughter's surname back to mine

Good day po. My partner and I are not married, and we have a 4-year old daughter. She carries the surname of her father. Just recently, we've been having problems and he claims my daughter is not his. Can I change my daughter's surname back to mine? What is the process? My daughter was born November 21, 2012 and applied for the acknowledgment in 2013.

Hello there. I am new to this forum hope someone can enlighten me.

I have just been married to a German national living in Germany. I have a minor child from my previous relationship and my child is carrying the last name of her father. I was not married to the father of my child.

Now that I am married, my husband wants to adopt my child. We plan on moving to Germany next year and since we are both working overseas, I know I need to apply for my FAMILY Reunion Visa from where I am currently located (hongkong). But my question is, while I have not applied for a reunion visa, can we start doing something to start the adoption of my child and carry the last name of my husband? So when we get our visa, we are all under one last name.
As an OFW, i have registered my last name already to that of my husband's. We are now after getting my child have the same last name as ours.

She is currently living in the Phils.

What are the challenges?

Thank you for helping me.
MORI