The phrase my name is Simpson, not Samson is uttered by a manual worker who is asked to lift or haul too heavy an object.

Most probably, Simpson is a generic name chosen for no other reason than its phonetic similarity with Samson, the name of the Hebrew hero of enormous strength whose story is told in the Book of Judges, 13-16.

The earliest occurrence of the phrase that I have found is from The Daily Mail (Hull, Yorkshire, England) of Monday 24^th September 1906:

One morning there went up to a foreman a weak-looking individual seeking a job. “What’s your name?” he was asked.—“Simpson, sir.”—“What?” —“Simpson, sir.”—“Very well, go and load that pig iron.”—The man looked at it, tried his best, and then going up to the foreman, he said: “I said my name was Simpson, not Samson.”

The second-earliest occurrence of the phrase that I have found is from the Camden Post-Telegram (Camden, New Jersey) of Thursday 10^th October 1907:

Too Heavy.

Hardware Dealer (to new clerk)—Oh Mr. Simpson, lift that anvil into the box and pack with it 500 pounds of trace chain.
New Clerk—Pardon me, but my name is Simpson—not Samson.

The phrase then occurs in Pictorial Humour, published in the Leicester Chronicle and the Leicestershire Mercury (Leicester, Leicestershire, England) of Saturday 2^nd May 1908:

Unscriptural Injunctions.
The Foreman: “Now I want you to carry out these packing-cases to the yard, an—”
The Labourer: “’Ere, stow it, guvernur. My name’s Simpson, not Samson.”

The U.S. cartoonists Gus Edson (1901-1966) and Irwin Hasen (1918-2015) made a character named Simpson use the phrase in this instalment of the comic strip Dondi, published in The Spokesman-Review (Spokane, Washington) of Thursday 22^nd February 1962:

With the motel business showing signs of prospering, Colonel Suggs hires a handy man.
“I betcha you’re almost as strong as my dad.”
“I do all right.”
“GI’s are the strongest guys in the world. My dad was one. Were you?”
“You ask too many questions.”
“The lad was only making conversation.”
“Yeah. I’m sorry, I just meant to say my name’s Simpson, not Samson.”

The phrase occurs in the following poem, published in The Limerick: 1700 examples, with notes, variants and index (New York: Bell Publishing Company, 1969), edited by G. Legman—this poem is from Lapses in Limerick, an oral collection made at Ann Arbor, Michigan, from 1938 to 1941:

There was a young lady named Ransom
Who was rogered * three times in a hansom.
When she cried out for more
A voice from the floor
Said, “My name is Simpson, not Samson.”

* Here, the verb roger means to have sexual intercourse with—from the slang use of the male forename Roger to denote the penis.