Yes, you can. Once you do, you can then proceed to change the name on your other government IDs. The Philippines has two laws related to the change of first name as discussed briefly below.
While more popularly known as the Clerical Error Law, it also allows you to change your first name at the civil registrar without need of a judicial order. No courts, judges or lawyers. Just you, some fees, legwork, and time.
Note: It amends articles 376 of the Civil Code so that your first name can be changed without a judicial order in cases specified by this law. You should attempt a petition with the civil registrar first before attempting to petition through the court.Join my Facebook group to get The Checklist: Everything You Need to Prepare for Changing Your Name.
This law lets you file your petition for name change with the court. The process is outlined in Rule 103 of the Rules of Court.
Note: You can change not just your first name, but your surname as well. The Supreme Court has previously ruled that children can use the surname of their mother instead of their father. Another case lists down some recognized grounds for change of name.It's currently improbable without a change in the law. In 2002, Mely Silverio, a trans woman, petitioned to change her first name and gender marker. While she was initially successful and her petition granted by the trail court, but the Office of the Solicitor General (OSG) filed a petition for review of the lower court's decision. Ultimately, the Supreme Court ruled that you can't change your name or gender marker on the basis of sex reassignment or equity. You can read about her case here: G.R. No. 174689 - Silverio vs Republic - October 19, 2007
But before the Silverio case, RA 9048, and RA 10172 (approved August 15, 2012), trans women like Geraldine Roman and Wesy Quisumbing were able to change their first names and gender markers following gender confirmation surgery in ~1994 and between 1996 & 2002, respectively. Wesy Quisumbing even got married to a man in Cebu (on or before 2002).
Note: Even ordinary trans citizens changed their names and gender markers around this time in the lower courts.You might be able to through the courts. Jeff Cagandahan, an intersex person with Congenital Adrenal Hyperplasia (CAH), was able to change his first name from "Jennifer" to "Jeff", change his gender marker from "female" to "male", and even got married to a woman. You can read about his case at the Supreme Court E-Library here: G.R. No. 166676 - Republic vs Cagandahan - September 12, 2008. But laws are finicky things so, more specifically, if you have CAH and self-identify as a gender other than that assigned to you at birth, you can. But if you have a different intersex condition, it's up to the courts.