I agree it could be an 'r' as well, with just a tail he signs with. Could be -ler, -ley, -ly, and more. We also have to consider that the big slash could be an 'x' 'y' or even 't'. Does that next letter have to be an 'l'?
Here's another thing that is hard to see in the pic unless you zoom in is that the left-side is not a letter fading, it's a pen that stopped working. If you follow it through you can see it come down, loop back up again into a line, but the line that could even be the 'i'.
I noticed on the page there is also the scratching/indentation of trying to get a pen working. He didn't go back over, and probably never finished that first letter. It could be a P, R, B, J, Ji, L?.
So he likely never completed that first letter—and wrote that 'dot' and the rest of the name, with a new pen, or getting the pen working.
What still gets me most is that it's doubtful anyone would sign 1 name. I think there has to be an initial there, or else it's a nickname that would be well-known.
I'm hoping someone has as much interest in cracking this mystery as me, but I'm really doubting it. 
Any opinions are appreciated, at the least I think it's fun.