Change my son's surname, to my surname, is that possible?

Hello there! I have a 1yr old son, I am not married and on my son's birth certificate, his father signed an affidavit that he is acknowledging his son and is allowing him to use his surname. My son's father is a supervisor in a semiconductor company and is giving monthly support which is like 3,000php only, sometimes, not really money because he will go here bringing milk and some groceries! And I bet, he's only doing this because we have an agreement notarized by a lawyer, that he should give monthly support to our child. I say so because before, he only gives his monthly support if he wants to and he always has an alibi (like his sister's allowance and tuition fees). One time, i texted him to surrender his paternity rights and asked him that, if it’s possible, i would like to change my son's surname, to my surname...I would just like to know if it is possible to do this?
Another thing is that he seems to misunderstand my text message which is to change my son's surname, to my surname, and if that's possible, i will no longer ask him for any support to our child. Due to this text (which he used maybe as evidence), he went to another lawyer, not the lawyer who made our first agreement, and seek for an advice maybe on how to surrender his paternity rights...
He went to our house yesterday, giving this letter, notarized by a lawyer, asking me to have my signature on it... The letter says that, he will no longer give any form of support to our child. Does my ex boyfriend did the right action regarding this matter, or did he bypass our first agreement??? Because I think, he didn’t let the other lawyer know about our first agreement??? Please help... Thanks!

the remedy is for you to adopt your child.

what will you get in return for that agreement? it is void as to the part about support because support cannot be waived.

how much will it cost if i will adopt my own child? and how long will it take for the processing?

Does it mean that the document which my ex boyfriend want me to sign is void???

Thanks...