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]

[mid–late 19C] (US) a phr. used on leaving a place or party suddenly.