I can’t give you percentages. But here’s the general procedure (at least in New York).
You get arrested. You’re identified. You will then generally be known to the legal system by that name.
I knew a prisoner who had a woman’s name. Why? Because he was with his girlfriend when he got arrested and, in an attempt to conceal his identity, they swapped ID’s. So he ended up being arrested under the name he identified himself as, which was his girlfriend’s name.
Most arrestees produce some identity, like this guy did; even if it’s just saying what their name is. If they refuse to give an identity, it can usually be found via fingerprints or other means. In the unlikely event that an arrestee doesn’t identify himself and can’t otherwise be identified, he’ll be listed as John Doe for record keeping purposes.
It is possible for a prisoner to get his name of record changed while he’s in prison but it’s a somewhat difficult process. Most prisoners using a different name than what they regard as their real one just let it go.
Once a person gets out of prison, they can call themself anything they like. They can use the name they had in prison, revert to some name from earlier in their life, or start over with a new name. That doesn’t mean that their history disappears; the records of their arrests and convictions follows them to their new name. But it might help with their public image if their crime was famous. Karla Homolka, for example, changed her name after getting out of prison.
Unless the person is fresh off the boat (or over the wall) they likely have some history in the country. AN interesting question might be what percentage of arrestees were never processed as juveniles. Once you’re in the system, you’re in the system, and juveniles are less likely to think “maybe I can stay unknown” and also not be looked for by parents. As Nemo points out, once they do arrest you, whatever they call you, you’re “the guy with these fingerprints”. Plus, many people are carrying a wad of ID - credit card or bank card, driver’s license, assorted other cards, fingerprinted when you join certain organizations, etc. It would be dumb luck or real planning to not get picked up with ID. Even in a big city, there is usually a Pareto principle at work - 80% of arrestees are from a 20% of the population. Most criminals are habitual.
So I’m going to make the educated guess that the number of unknown is very low, and the majority are recent arrivals.
We’ve had thread before on “how do you prove who you are without documentation?” The short answer is, today everything you do leaves a data trail and it’s hard to fake the total trail. The only question is who wants to link these data breadcrumbs into a single trail, and how much effort they will take.
you can for example change your name once you get out of prison. But, the police will always have a way to connect your name with your fingerprints, as will any job that requires a background check. Can you change the name on your school diploma or birth certificate? Job history? Last 5 addresses? Financial institutions, tax record, credit cards and banking. There’s a plausible reason why one or two might be blank, but all of them? As Jennifer Lopez says to Jason Statham in “Parker”, “I ran a credit check on your name, and guess what? Until 6 months ago you didn’t exist.”