
He was treated by Dr Samuel Mudd. Mudd was a Maryland physician and he was later implicated and imprisoned for aiding and conspiring with Booth in the assassination. Hence, it was said of someone who was unpopular or the victim of defamatory charges “His name is Mudd.”
However, 'mud' in the sense of scandalous or defamatory charges goes back much earlier. There was an expression, 'the mud press,' to describe newspapers that besmirched people's reputations by throwing mud, as long ago as 1846. And the phrase itself first appeared in print in 1820, 45 years before Lincoln's assassination.
But the American explanation was fun while it lasted!