Thanks for posting that history.
Dr. Mudd was not a part of the Lincoln assassination. He provided medical care (of a sort) to one of those allegedly involved.
I have heard that the saying “his name is mud” is directly connected to what happened to this Dr.
He actually later was pardoned because of his work at the prison. They had a yellow fever outbreak and the forts physician died and left him as the only doctor left. He identified the problem and treated everyone with success. Hence his life sentenced was reduced to four years.