Welcome back to the Wefugees Community and thank you for reaching out to us again.
If I remember correctly from one of your last questions, the paternity issue was subject in court proceedings, right? I am neither a lawyer nor a specialist in family law, but I assume that if the authorities already know about the father (latest through a mandated/official DNA-test), it might be difficult not to name him as the father of the child in the birth certificate. Additionally, it can get complicated in case you want to apply for certain allowances (as the so-called "Unterhaltsvorschuss" if the father is not supporting the child financially). Eventually it may also be in the child's interest to learn about his/her father later.
However, you can always keep the sole custody of the child - is that also an option?
In any case, please don't hesitate to get back to us with any further questions.
All the best,