First, the purpose of a GMRS callsign is to identify yourself and your station on the air. There is an official protocol required by the FCC for doing so, and some general etiquette to follow. Read this post in the forum for both.
As for repeaters, the repeaterbook on CHIRP is primarily intended for ham radio operators. The go to resource for GMRS repeaters is myGMRS.com. You will need to create an account and login for full access to the repeater database, but it’s easy.
Most GMRS repeaters are owned and managed by individuals. Some of them are intended for their private use, and others are available for public access, however many will require permission from the owner first. The myGMRS.com database will usually include contact information for this purpose.