Previously, I have seen a description in a book explaining business manners to the effect that “a letter written in red is an expression of intent to be isolated to the other party.” I've forgotten what book it was.
I was in my 40's when I was reading this book. Therefore, in my life up until then, I had a cold sweat when I thought that I might have been receiving “a statement of intent to insulate (even if I myself had no intention of insulating at all).” However, in that book, “Why is it a statement of intent to insulate?” The reason was not specified.
When I searched for “red letter manners” on the internet, I asked the library about this question and got an answer.
http://crd.ndl.go.jp/reference/modules/d3ndlcrdentry/index.php?page=ref_view&id=1000083249
It's helpful, but there's no clear evidence. What I can guess in my own way is that red letters are used for scoring, correction, review, etc., as there is the phrase “insert vermilion.” Writing in red letters means scoring, correcting, and reviewing from a higher standpoint. Therefore, I think it's probably safer to write in black except when “putting in vermilion.”
Other than that, various reasons have been given, but the evidence is vague, and it seems that there are many others that are rather doubtful. For example, when I searched on the web, the viral media site called grape said, “Why can't you write your name in red?” There was an article called “There were quite a few people who didn't know the reason,” but it wasn't a very reliable description.
https://grapee.jp/224260
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Indicate a dead person
When a name is dug up on a tombstone while alive, there is something called “vermilion” that turns the name part red.
In vermilion, it means “still alive,” and it seems that the impression that “bad luck is bad because it is associated with a tomb” came from there.
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It's a description that amplifies misinformation.
If you receive the commandment during your lifetime, you will usually engrave your kakana on your tombstone. In that case, only the two-letter part of the actual kaima part will be reddened with paint. Turn it red to indicate that it is alive. It's definitely not ominous, and it doesn't “indicate a dead person.”
The name part of the question is in red, but it's probably the “meaning of pointing out” that you should be careful about how to write the name.