For a Nimae the act of birth and the act of recieving a name turns to one and same thing : that symbol that is carved into the whiteness of its cold ceramic flesh, draining the initial energy into it and allowing the unliving to become alive. That would be one of the 60 sylbols of the ancient alphabet alchemists still make use of for their tricky crafts, chosen carefully and for a reason. Rei - is just one of those.
That symbol is the name the Nimae will carry until it is decided to gift him with another rune, but that is only if its destiny is to become a Machina, otherwise the Nimae will remain nothing but a Golem with no purpose.
A Machina can recieve up to 12 symbols, each one symoblising the spirit it is supposed to become a host for; each one comes along with a thorough upgrade of the artificial being both of it's body and mind.
Rei is one of the 60 symbols, and this is how it gives now Birth :
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