There are two orphanages in Konoha: Enshoku House in the southwest–between the Hyuuga and Aburame holdings–and Ryokushoku Institute in the northeast–between the Akimichi district and what used to be Uchiha land.
Not that their proximity to cardinal clan territories have much influence on which orphans end up where, it’s just the easiest way to differentiate the two. That and the fact that most orphans from Enshoku tend to wear shades of red while those from Ryokushoku wear shades of green.
It must be a subliminal influence; Tetsuki certainly isn’t basing her fashion choices on nonexistent fond memories of the place.
Though perhaps that’s a bit harsh. Ryokushoku was hardly torture, and she knows that orphanages further from Konoha’s reach and subsidies aren’t as professionally run.
But maybe that was the problem–it was too well run, too clinical and cold and objective. They weren’t family, they weren’t students, they were barely even wards of the state–they were resources, potential products, and future soldiers. A mass assembly line of moldable children without anyone to care for their well-beings outside of what makes them useful.
Technically, six year old orphans aren’t mandated to join the Academy, but if they haven’t been adopted by that point then there aren’t many options left: very few orphans show an aptitude for a strictly civilian vocation that would induce government sponsorship for Shougakkou. After that, frankly, between the red light district and urban legends of ANBU stealing children in the middle of the night, the Academy is the safest bet.
Her Academy file had her name as Ryokushoku no Tetsuki until she was ten, when she updated it along with her new address–moving out from the orphanage as soon as she could even remotely support herself. Her life path thus far is in no way unique, but at the very least she has heard of others.
None of that helps in figuring out Naruto Uzumaki’s situation.