my daughter has no fathers name on her birth certificate and my significant other now I have 4 children with wants to give her his last name is that p

Having practiced family law in this state for the past 34 years, I can tell you that I have seen too many "murphy's stories" to simply tell you to change the birth certificate to identify your significant other as her father. Someone else may tell you that it is the easiest and cheapest way to go in this setting, but the risk is that one day, someone comes out of the blue, claiming to be her biological father and seeks an order of the court for a determination of parentage and visitation. Yes, I have seen those settings and they can be very stressful. The best way to handle this issue is to formally file an application with the court to permit your signficant other to adopt your daughter. To do so though, will require you to provide notice to the person[s] you belevie may have been the biological father so that his rights can formally be terminated. If you know who is the biological father, you can ask him to sign the paperwork in advance permitting the termination of his parental rights and as part of that same proceeding, ask that your signficant other be permitted to adopt your daughter.  I cant tell you that you need to handle it formally but if you have any fear that someone may assert any claim to be her biological father in the future, the best way to handle it is to have his rights terminated once and for all.