try mo muna sa town registrar kasi madali dun, since space lang naman ang error, baka i-approve na yan, if not then tsaka ka nalang mag-file ng court order which takes a more time to process.
edit: for first name error only. the info on the links that hifi provided are correct. if it's a simple clerical error and can be seen clearly on the face of birth certificate, your remedy is to make a petition and send it to civil registrar where your niece was originally registered. the civil registrar there is empowered to make the correction. there should be no need for a judicial petition. of course matagal pa rin proseso, but at least it doesn't have to go through the court.
a possible remedy would be for her to adopt the misspelled name on the birth certificate and and ask the school to change their school records. many schools allow this since they know of the problem. hope this helps, good luck! it's strange to have to use a different name, but many people adopt this simple solution.