Fixer,
I have covered, and photographed many bill signings. President Trump mostly uses one pen, other presidents use many pens signing a small portion of their name, with each pen, I have seen what look like twenty that were being used at different events. They are then given to the authors of the bill, and other guests in the ceremony. President Clinton gave me one at a ceremony in California years ago. He also told me for a bill to be officially legal a president must sign his full name, no initials, spelled all the way out, or the law does not go into effect.
Bush, Obama and Trump, at least the ones I have seen never did that. I don't know if Clinton was right, however, he was in a very good position to know that, and I would not doubt him.
One thing I have never seen other presidents do is what President Trump does is after signing the bill is to display it to the cameras and audience. At least the ones I have witnessed. I like that.
The Quill pen you mention, I believe is an old tradition at the Supreme Court, when a case is heard, the attorneys arguing before the justices receive a quill pen as a memento of trying a case before the court. Don't hold me to this, maybe there is a lawyer here who may know their traditions better than myself.
One thing about presidential events I have noticed over the years is that things are the not always the same. There are minor changes to things and no explanation is offered. And things change from administration to administration, and the Pen thing seems to be one.
The surrender of WW II, was held on the deck the battleship USS Missouri, and General Douglas MacArthur Signed for the US, and a delegation of Japanese officials represented Japan. I think just a regular pen was used. At that point, they were all just glad it was over.
Hope this helps,
Your pooler,
RL