HELLO! I have a question. The Mach wiki says that “Ostrum” in Mach’s name is how she signs, and probably a nickname. Is that true or is Ostrum part of her actual name? I trust you WAAAY more than the wiki.
THIS IS A VERY GOOD QUESTION!
Ostrum is her legal middle name. It is what her great-grandfather called her, and it's a very widely accepted headcanon that she distances herself from that name and either signs that way out of habit or because she is required; or the signature in the system is automated.
Ostrum is very much NOT a nickname. Her name is codified as COM011066, essentially confirming that Ostrum is a legally identifying name. It is much more likely that the purple coloring scheme came from the name and not the other way around.
Interestingly enough, though, I recall seeing her have a phone call where she says the name first thing. This call isn't documented on the wiki, and I don't really remember anything else about it.
It throws the widely accepted thing into question, unfortunately.