What tyto do if I’m looking to adopt my fiance’s son?

Even though the father's name is not on the birth certificate, your fiance' knows who the father of the child is.  Before she can proceed with an adoption, she will have to terminate his parental rights to the child.  If she filed a petition claiming to not know who the father was, when she actually did, she could face contempt or criminal charges for the false entry.  His name not being on the birth certificate does not negate the fact that there is an identified biological father. 

Some people have tried to file petitions alleging an unknown father and have rights terminated.... only to have the father come back several years later to undo an illegal adoption.  If you really want to be the father of the child, you and her need to proceed forward and cross the "i's" and dot the "t's".  The last thing you want to do is have to explain to this child five years later who this stranger in his life is because of a hasty adoption.

So... first step is to let biological dad stay in his non-committed role.  Your fiance' has reached out and he has rejected the opportunity to be a part of this child's life.  His abandonment will help when your fiance' petitions the court to terminate his rights.  The Texas Family Code authorizes the termination of a parent's parental rights for abandonment.  Second step is to establish a sound home for the child.  Even though it sounds harsh, it will really help if you get married first and spend a few months as a family unit before moving forward with the adoption.  You want to have things situated "homewise" before you file because the court will order a homestudy -- which is essentially an inspection of your family lifestyle.  Once you have a little time together, your final step is to file a petition for adoption.  This can and will need to be combined with a petition to terminate the biological father's rights.  Bio dad is only required to receive notice of the adoption/termination petition---there is no requirement that he consent to the termination or adoption in Texas.  If he follows his current pattern, you may be able to terminate his rights by default or by agreement.  After his rights have been terminated, the court can then proceed with the adoption if they find that it is in the best interest of the child.  From the time that you file the petition to the time that the judge enters the final order, can take anywhere from a couple of months to a year---depending on whether or not biological dad decides to fight the termination.  Obviously, if he defaults or consents to the adoption it will go much quicker. 

You are not required to have an attorney in this process, but it will help if you can work with a family law attorney to ensure that all of the proper procedures have been followed.

If there is a birth certificate listing the father of the minor as such or a court decree then the only way that you can adopt the minor is through a court ordered adoption where the actual father gives up his rights via a court order to the minor child. I suggest that you consult with a family law attorney about the matter you are writing about.