Remember, the story wasn't published until “1885” and it was penned sometime shortly before this. “If” whoever penned it was actually looking for that person with the “missing paper” then they would almost be forced to use the “real name” identified with that missing paper, or Thomas Beale. In reality, back in 1817-1822 the individual who had actually stayed with Morriss could have gone by any name, Thomas Beale himself perhaps having never stepped foot in this country, the entire affair in the states having been conducted by family, etc.
This is just another reason why I'm certain that the letters are bogus, a simple cover story for what may have really transpired back in 1817-1822. It's also one of the reasons why I feel pretty certain that C3 will contain names closely associated with the Beale family. And yes, I also believe the Thomas J. Beale of Richmond is strongly associated with the story, if in fact he wasn't the actual author in search of something with Ward's help, that family secret he still believed to exist. I'm fairly certain that the possible answer is something along these lines of thought. This is also why those letters are closed with only TJB and also why the alleged Morriss description subtly references a free man of color named Thomas J. Beale.