You have different levels of witness protection, but I assume you are talking about the most advanced, which would be WITSEC run by the Department of Justice and the US Marshals service.
Before the person testifies, USMS would be responsible for protecting the person and in coordinating with the local police agencies, would be responsible for getting them to and from trial to testify.
After they testify, USMS will relocate them to a different location and will provide them with back stopped identifications. These are not fake IDS, they are real IDs issued by people within the Federal and State agencies that assist with the program.
Basically, those agencies add this new identity to their databases and may backstop it (create archived information to show the person has existed and wasn’t just created out of thin air) this way nobody, even other people from that agency, would know it was a fake identification.
They would obviously then be issued legitimate documents under that created identitity such as social security cards, birth certificates, maybe driver’s licenses, and even some other stuff such as high school diplomas and other stuff possibly needed to help them get work, get their kids into school, etc.
They would be coached by their coordinator regarding their and their families new identifications. Basically, name, date of birth, and their new identities history. Practicing signing and writing their new name so they don’t accidentally sign their old identity on a credit card receipt or something.
The majority of these people are criminals themselves and about one if five of them are subsequently arrested again in WITSEC which causes a problems for the program and may require intervention from WITSEC. The most infamous example of this was mob gangster associate Henry Hill (Goodfellas), who was arrested after spending years in WITSEC.
A person can leave WITSEC at anytime, the program is completely voluntary.
The persons family is often allowed, and encouraged, to join the person in WITSEC.