You know what's always struck me as really, really interesting?
We know that they used to be in the same position as Lake, reflecting a prime. It's pretty clear that reflections, while acting as a reflection, definitely don't have names, or else Lake would have picked one for themself the first chance they got with how independent they are. If it was even remotely an option they would have gotten one, but it clearly wasn't
Lake lays out the choices a reflection has when their prime dies pretty clearly, either get memory wiped and stuck to a new prime, or become a fleck. And it seems like there are a lot of benefits to becoming a fleck
The biggest one being you get an identity.
Mace doesn't even deny it. He tells Lake that becoming a fleck wasn't about keeping his identity, but he doesn't say he doesn't have one. He never pulls the card that him and Lake are exactly alike, that they're both only there to support the balance. He clearly looks down on Lake, insisting from the very beginning 'that sliver isn't a person' but neither of the flecks seem to have that same sort of view of themselves
Sieve is confident introducing himself and Mace by name, but there's an obvious hesitation and annoyance in his voice at even calling Lake 'MT' which is just a shortening of Mirror Tulip. Sieve even thinks enough of Mace as a person to throw away fleck protocol after Lake kills him, it's undeniable that they see themselves as people just as much as Lake sees themself as one
And it's so interesting how sharp that distinction is. Sieve and Mace were just like Lake at some point! Just like every nameless, interchangeable reflection before deciding to become flecks.
Mace can say it wasn't about keeping his identity, but it still gave him one. It still allowed him to see himself as a person in their society, and probably even more importantly for the flecks, to see themselves as above those who aren't people.
It also adds even more weight to Lake's decision to break free entirely. Because they could have just... waited. Sure, it would suck, but they could have played by the rules, been Tulip's reflection for her life and then become a fleck and be granted an identity. They know that's how it works, and it would have been the easiest option.
But Lake never even considers that, because they don't want to be a part of that system. They don't believe they need to earn an identity, earn the title of 'person' by becoming a fleck. They're already a person, and they aren't going to wait for the mirror society's approval to cement that as fact.
