Using middle last name in a letter?
My apologies if this question is a bit too straight-forward, I don't know where else to ask this, or if this is even worth asking. I have seen a (fictional) letter with a signature of a person unknown. Not sure if I should share the full detail, so I'll just use this as an example...
If a person's full name is John Quincy Smith, one would think this person would sign his full name on a letter. But let's say there was a letter was signed "Q. Smith". Would this be considered correct? Would we be talking about the same person, or potentially a different person? Granted, there is always the idea that anyone can sign under any name, but for the sake of argument.
Any help would be greatly appreciated!
ETA:
Someone made a really good point: "are we sure the letter is a Q and not a stylized J?"
Upon reflection, I think I made a mistake and probably should have used an example to better fit my issue at hand. The name I chose wasn't exactly close. Replace the initials "J.Q.S" with "H.J.B". Like..."Henry Joe Black"? Sorry for the poor example. So to revise my original fictional question with the new name and better details:
There is a person known as "Henry Black" - mainly known as "Mr. Black" to most, but known by his first name "Henry" to a few. As far as I know, his middle name is unknown, and his family history (i.e. if they share the same name) is unknown. And this letter which has "J. Black" as the signature, is a random letter, not an official document nor a letter to a dearly loved one. That is about all I have as far as the details go.
Bottom line question: Would "J. Black" be one person's full name "Henry Joe Black"? Or would it be reasonable to presume "J. Black" is a different person?