I tried to fix(...) the translation for Tojiko's line (蘇生の蘇にわれ、いにしえ自分を屠ると書いて-
蘇我の屠自古です) to make it more in line with Enlgish context. I think it flows a little better, but it does change the overall structuree. Given that Chinese characters are ideogram, it is pretty normal in East Asian countries to explain how to write (or read) your name, but such conventions are not common in western countries so far as I know.

Here's the work by previous translator, so please feel free to revert back to it if you find mine more awkward:

蘇生の蘇にわれ: Written with the 'so' of 'rebirth' with 'me'...

古の自分を屠ると書いて: ...slaughtering my ancient self.
Soga is describing how to write her name: the same character for 'so' (蘇) as in rebirth (蘇生), the 'ga' (我) meaning 'me', the 'ko' (古) meaning 'ancient', the 'ji' (自) from 'self' (自分), and the 'to' (屠) of 'to slaughter' (屠る).

蘇我屠自古です: Soga no Tojiko.