“His/Her/Your name is Mud” is to say that someone is discredited or unpopular. The saying was defined in the book Slang: A Dictionary of the Turf, the Ring, the Chase, the Pit, of Bon-ton, and the Varieties of Life (published in London in 1823):
 
”Mud—a stupid twaddling fellow. ‘And his name is mud!’ ejaculated upon the conclusion of a silly oration, or of a leader in the Courier.”
 
It is sometimes said that “name is Mud” comes from Dr. Samuel Alexander Mudd (1833-1883), who attended to John Wilkes Booth after the 1865 assassination of President Abraham Lincoln. However, the phrase uses the name “Mud”—not “Mudd”—and had been in existence at least ten years before Samuel Mudd was born.
 
“Name is Mud” was cited in U.S. newspapers only from the 1870s. “Jim, your name is Mud” was printed in The Daily Inter-Ocean (Chicago, IL) on January 24, 1875. “Your name is Mud” was printed in the Detroit (MI) Free Press on June 20, 1876.
 
     
Wikipedia: Samuel Mudd 
Samuel Alexander Mudd (December 20, 1833 – January 10, 1883) was an American physician who was imprisoned for conspiring with John Wilkes Booth in the assassination of President Abraham Lincoln.
(...)
Samuel Mudd’s name is sometimes given as the origin of the phrase “your name is mud,” as in, for example, the 2007 feature film National Treasure: Book of Secrets. However, according to an online etymology dictionary, the phrase has its earliest known recorded instance in 1823, ten years before Mudd’s birth, and it is based on an obsolete sense of the word “mud” meaning “a stupid twaddling fellow.”
 
(Oxford English Dictionary)
mud, n.
colloquial. A fool, a simpleton. Obsolete.
1703   Hell upon Earth 5   Mud, a Fool, or thick skull Fellow.
1823   ‘J. Bee’ Slang 122   Mud—a stupid twaddling fellow.
colloquial.  [Compare sense 8.] one’s name is mud (also Mud): one is discredited, in disgrace, or temporarily unpopular.
1823   ‘J. Bee’ Slang 122   Mud, a stupid twaddling fellow. ‘And his name is mud!’ ejaculated upon the conclusion of a silly oration, or of a leader in the Courier.
1887   Lantern (New Orleans) 16 Apr. 2/1   Zeller wants to be Recorder..but his name is mud.
   
Google Books
Slang:
A Dictionary of the Turf, the Ring, the Chase, the Pit, of Bon-ton, and the Varieties of Life
By Jon Bee (John Badcock)
London, UK: Printed for T. Hughes
1823
Pg. 122:
Mud—a stupid twaddling fellow. “And his name is mud!” ejaculated upon the conclusion of a silly oration, or of a leader in the Courier.
   
Google Books
Spirit of the Age Newspaper, for 1828
London, UK: Published by A. Durham
1829
Pg. 60:
‘Pon my life ‘tis true,
AND MY NAME is MUD.
(From February 3, 1828, The Age, London, UK, pg. 38, col. 3.—ed.)
 
24 January 1875, The Daily Inter-Ocean (Chicago, IL), “Another Tragedy,” pg. 8, col. 1:
“He refused, when I said to him, ‘Jim, your name is Mud.’ He called me a bad name, when I struck him.”
 
Newspapers.com
20 June 1876, Detroit (MI) Free Press, “The Campaign Opened,” pg. 3, col. 3:
“His name isn’t Aze any more than your name is Mud.”
 
OCLC WorldCat record
The Burlesque, vol. 1000, Richmond, Va., Feb. 19, 1910 : I dare you to kid his honor the mayor or blaspheme the courts of justice : if you do your name is mud.
Author: John C Bauman
Publisher: [Richmond, Va.] : [publisher not identified], [1910]
Edition/Format:   Print book : English
 
OCLC WorldCat record
My name is Mud You’re getting all over me
Author: James O’gwynn
Publisher: États-Unis : Mercury records, [1962]
Edition/Format:   Music : 45 rpm : English
 
OCLC WorldCat record
Concrete and clay ; My name is mud
Author: Eddie Rambeau
Publisher: New York, NY : Virgo Records, [1962] ℗1962
Edition/Format:   Music : 45 rpm : English
 
OCLC WorldCat record
Our name is Mudd : the Patrick Michael Mudd family line from 1647 to 2011
Author: Anastasia Meinert Mudd
Publisher: Blurb Inc., 2010.
Edition/Format:   Print book : Preschool : English