Green’s Dictionary of Slang

my name is Haines phr.

[an encounter between President Thomas Jefferson (1743–1826) and one Haines or Hanes, a fanatical opponent. Haines, not knowing the identity of his companion, vilified Jefferson in extreme tones as the two men rode side-by-side near Jefferson’s home in Virginia. When they arrived at Jefferson’s home, the president, affronted but still courteous, invited Haines in. Only then did Haines ask his putative host for his name: ‘Thomas Jefferson’. ‘Well, my name is Haines,’ replied his opponent, before riding promptly away]

(US) a phr. used on leaving a place or party suddenly.

[US]Spirit of the Times (N.Y.) 18 Apr. 77/3: ‘My name is Haines’ enjoys a popularity which no other slang or cant phrase has ever attained. ‘I’m o-p-h,’ ‘I must mizzle,’ ‘I must make myself scarce,’ are frequently used, but the expression which heads this article leaves them all out of sight.
[US]Vicksburg Wkly Sentinel (MS) 27 Feb. 3/1: I see [...] that Count Weiss (so called) is posted among the ‘my name is Haines’ gentry.
[US]Daily Empire 6 Mar. 4/1: ‘My name is haines,’ said Sam, but then Sam. was drunk and disorderly.
[US]Schele De Vere Americanisms 608: Haines, my name is, a slang phrase used to express, I must be off, I am going at once – originated in an incident in the life of President Jefferson, and is still in use.
Locke’s Nat. Mthly 1 534/1: He rose [...] and leaning a moment upon the butcher's arm, muttered, with a ghastly smile, ‘Boys, my name is Haines, and I’m off’.