Changing Names

Good Day !!
I am 25 years old single mom.
I gave birth last April 11, 2005
At that time my mom asked me to put their names as the Parent of my own child. I was 18 years old at that time and I can't make my own decisions so I agreed with them.
And Now that I am 25 years old working as an ESL Teacher.I would like to change my baby's name to my name and Her father's name. Would it be possible? How can I change It?

HI! Good day!! tungkol po ito sa name ng father ko sa aking birth certificate,kasi po noon kumuha ako ng passport 2011 hinihingi nila yung birth certificate ko from NSO but they ask my local birth certificate dahil blurd yong NSO ko...nakakuha ako ng passport ...ngayon nag asawa na ako lahat ng dokomento ko ay LAURENCIO instead of LORENZO I never used Lorenzo since when I was studying from elementary to college... required naman yong NSO but they asked supporting document because they cant read my NSO is blurd thats why i thougth its ok , ngayon talagang meron problema we knew that my father's name is different ,I married July 28, 2012 the requirements is NSO birth certificate and others...they found on my birth from local is different from NSO,they asked my baptismal,certification of confirmation,and marriage contract but the same of my local certificate....nag pa red ribbon ako sa aming marriage contract and my NSO birth certificate but i dont know yet if its ok yun...very strict ba cla sa fathers name ko ? ano ba ang dapat gawin?
para maitama ko yon ... thank you very much wait to your response...
marilyn

and also I was attend the CFO seminar this wekkend required po nila ang birth certificate from NSO but wala naman silang tinanong sa tungkol sa aking BIRTH CERTIFICATE...binigyan nila ako ng(CFO certification ) wala naman problema ehh..i need advice as soon as possible...i always check your response

thank you so much
marilyn