I'm not entirely sure how it works inside, I just know the reason my brother-in-law has a modified name on Facebook. As for the inmates, they obviously all have numbers but any prison guard can look them up in the computer.
Fun fact: Portions of the numbers on an inmate's chest refers to things like the year they entered the prison, what number they are for the year that they entered, what they're in for and either how long or when they get released.
The only problem with forcing real names that I've recently encountered are family members who work in prisons. They use a modified name as to make it difficult for an inmate to gain knowledge of them and where they live. Personal and family protection in a way with the ability to still use Facebook to connect with distant friends and family members.
Fun fact: Portions of the numbers on an inmate's chest refers to things like the year they entered the prison, what number they are for the year that they entered, what they're in for and either how long or when they get released.