A criminal case if filed in court already is always captioned People of the Philippines against the accused because the law violated is the law of the Philippines.
The complainant (properly called private complainant) is not named in the title but mentioned as the Information (Information-yung documento kung saan nakasaad ang paraan kung paano ginawa ang krimen, sino ang gumawa, kelan at saan ginawa at kung sino ang pribado at publicong nagsasakdal). ang Pribadong nagsasakdal ang yung mismong nagrereklamong tao samantalang buong Pilipinas naman and public complainant.
The usual procedure is that the court will issue an Order of arrest and a warrant of arrest at the same time if the accused is not detained or have voluntarily surrendered and posted bail. Ang gawin mo lang bago ka hulihin ng pulis eh magsurrender ke sa korte tapos magbayad ng piyansa sana ka lang nagtataka ako kung bakit nilagay na no bail yan.
If i were your lawyer (note that i am not a lawyer, just a student), i would explore the possibility of filing a motion for determination of probable cause with urgent motion to lift warrant of arrest. In the alternative, it could be possible also to simultaneously surrender (you) with motion to set bail because estafa is a bailable offense and it would be gross ignorance of the law to deny bail in estafa. Kung hindi namam naghuhuli kaagad ang pulis ay pwede ring lapitan ng counsel ang clerk of court or judge then politely point out that you would like to post bail but they inadvertently indicated no bail in the warrant. It is possible that the clerk III or stenographer made a draft of the warrant and the judge and clerk of court failed to notice the mistake.