Zenniwa

There is a recent topic on just this that may answer your question.

What is everyone's take on Acquiring U.S. Citizenship for your Child after adoption in the US. Per this link, it suggested that it is immediate. So after a step parent adopts a LPR step-child in the US and then becomes your child, the child becomes a US citizen right away? Just file N-600 to obtain certificate of citizenship? Acquiring U.S. Citizenship for your Child

Look at adopting the child AFTER they have completed the visa process and are in the USA, at that time you will need to follow the laws of the state where you reside.

This was discussed heavily in a prior post from 2 years ago and holds true today. The advice that is being given here is not currently reflective of the requirements for the Philippines law nor for USCIS/immigration.
 
http://www.visajourney.com/forums/topic/531798-adopting-niece-from-philippines/>
 
No problem adopting your nieces, what you are doing is not that uncommon in the Philippines.
http://www.dswd.gov.ph/programs/adoption-and-foster-care/
But the adoption process must be completed BEFORE do the visa process.
https://ph.usembassy.gov/u-s-citizen-services/adoption/
 
From <http://www.visajourney.com/forums/topic/611759-adopting-a-niece-from-the-pi/>
 
What does USEM say about adoptions http://www.visajourney.com/forums/topic/611759-adopting-a-niece-from-the-pi/?page=1
 
 
 

~~Moved to the Regional forum, from Effect of Major Family Changes - As the OP is asking about name changes and adoption. As the PI gives unmarried mothers sole custody and the fathers have no parental rights. This discussion is best handled with members familiar with both countries.~~

Its not as complicated as others have posted.
 
First- you asked about 2 different things. A name change and adoption. For the name change you will not be allowed to change the childs last name to yours upon marriage. While the laws allow for anyone to request a name change it has to be approved by the court. Courts will not approve you as the step father to give your last name to the child with out you adopting her. They view it as you getting a benefit (everyone having the same last name) with out you taking on any legal responsibility for the child.If you want her to have your last name you have to be legally responsible for her.
 
(You can look into the mother changing the childs name in the PI before she comes. If it is possible for her to do so you have to see how long it will take and make sure it can be done before the visas are issued so the new name is on the visa)
 
If she can not change the name in the PI or its too complicated or just not the path you wish to take and/or you still want to adopt the child you will do it in the US since you your wife and child will be CA residents.
 
Its called step-parent adoption. Laws vary. In CA in order for you to adopt the child you need the other parents consent. In this case the fathers. I understand there is no name on the birth certificate and the laws about illegitimate children there. This doesnt matter to the CA court. Like posted they will want to know who the father is. If you say unknown (and swear under oath you have no idea) they will do "research" to try to find the father including contacting potential fathers. However your post indicates you know who the father is (hes just not on the birth certificate). So you will not be able to state father unknown.
 
The court has specific processes for notifying the other parent. (dont be intimidated by phrasing like hauge convention) Its not a very difficult process to serve the father notice. Its just a very specific procedure. If the father signs off on it you are good to go. If he doesnt respond the court can terminate the father rights. The fathers rights must be terminated for you to adopt.
 
You can look into adopting the child in the PI before they move/ visas issued however that WILL be complicated. That would be an international adoption and no more k2. Because you already have the k process going youre better off sticking with the k2 process for the child and doing an adoption in the US. Your wife immigration status has no impact on the adoption process.
 
Here are some links to help you get started-
https://apeopleschoice.com/california-adoption/stepparent-adoption/
https://law.justia.com/codes/california/2009/fam/7660-7670.html
http://www.courts.ca.gov/selfhelp-adoption.htm

I just want to reiterate for future posters: California was used for illustrative purposes

Ah I thought you knew something I didnt! LOL
 
But anyway even though each state does things a little bit differently- I still think the advice is still valid. The links are not. OP google step parent adoption and your state to find more info.

And to throw a monkey wrench in the works, the Philippines is not a party to the Convention on the Service Abroad of Judicial and Extrajudicial Documents in Civil or Commercial Matters: https://en.wikipedia.org/wiki/Hague_Service_Convention#State_parties

Oops I should have clarified; I was NOT referring to the Hague Convention on the Protection of Children and Co-operation in Respect of Intercountry Adoption: https://travel.state.gov/content/travel/en/Intercountry-Adoption/Adoption-Process/understanding-the-hague-convention.html
IDK where OP will reside in the US but lets say California for illustrative purposes. In this example, OP will have to legally serve the birth father, as per http://www.courts.ca.gov/selfhelp-adoption.htm. But the birth father will most likely be outside US jurisdiction at that time. Thus the following will apply, http://www.courts.ca.gov/selfhelp-serving.htm#hague:

If you want to change the child's last name, you will need a court order.  Either in the Philippines or the US.  Probably easier in the US after she immigrates rather than in the PI.
 
With an step-parent adoption, you will need to notify the father since his parental rights are being terminated so you can be her legal father.  It doesn't matter if he is not listed on the BC.  Your fiancee knows who the father is.  If you want to adopt, you must terminate his parent rights and that requires notifying him.  No court would let you adopt without notifying the father that his rights are being terminated. 
 
Since this is a step-parent adoption, you do not have to adhere to the Hague Convention.

^^^These posts 100%. For example, if you have to legally serve the child's biological father it has to be through the Hague Convention: https://www.americanbar.org/newsletter/publications/gp_solo_magazine_home/gp_solo_magazine_index/oct99bur.html. That is just 1 of many potential speed bumps.

immigrate first, make sure the marriage is solid (several years), THEN worry about possible adoption

Immigration and adoption together are complicated issues. Not a DIY case......You need an experienced international adoption attorney.