Millions,
I’m serious. What’s wrong with “andersons,” or “smithies,” or “mcgillicuddies”? Was there a…particularly well endowed Mr. Johnson back in the olden days?
gutterminded,
birdmonster
If you used every name, it would be so diffuse as to be meaningless. That being said, it’s not as though “johnson” is that exclusive. There are plenty of generic names that stand in for “penis.”
John Thomas, Willy, Hodge, Dick, Peter, Jimmy, Louis, and Bob spring to mind. I’m sure there are plenty of others.
If you’re looking for a concrete answer, we could always make something up:
“16th century Patriarch John Thomas Hodge sired eleven sons, all of whom carried his genetic endowment of being built like a mule. His oldest son, Bob, was forced to flee to the New World colonies after the unfortunate death-by-haemorrhage of a mayor’s daughter. There, he took the name of Johnson, and continued what became the American branch of the category of human later recognized as h. macrophallus.”
Unfortunately, the correct answer is probably that there’s something in the human psyche that impels guys to indulge in microanthropomorphism when it comes to their soft bits, and some names just stick better than others. I call mine “Lousewort,” for instance – and nobody seems to emulate that.
I call mine “Lousewurt.” We’re blood brothers.
. . . Or some-kind-of-bodily-fluid-or-semifluid-brothers, anyway! 
Jimmy?
As in “She made me put a Jimmy on my Jimmy!”?
I’m not sure that would work.
And “Bob” just seems creepy.
I call mine MR JOHNSON
You should REALLY be calling it Priapism. I demand a change!
Not to mention the fact that a Johnson can be Randy, or even Magic.
But there it is. “I rogered her with my roger” seems a little weird, too, although I guess there are plenty of other words that double as nouns and verbs, like “hammer.”
As for the prophylactic sense of “jimmy,” “jimmy” also has a wider slang sense of “any mechanical contrivance,” but especially one used by burglars to get into difficult places. This sense of “jimmy” is related to a similar sense of “jack” as “a mechanical device.” It’s from this sense that we get the word “jackhammer,” and also “blackjack.” (A cosh, not the game.)
“Jack” is also used a male signifier for various animals (especially donkeys,) and of course belongs on the list of names used simply to mean “penis.” (We should probably touch on the term “Jacking off,” in passing.)
Let’s not forget Jack Johnson and Jimmy Rogers.
There is a well known race car driver in Australia called Dick Johnson.
Ohhh, you can call me Ray, or you can call me J, or you can call me Ray J, or you can call me Johnnie…but ya doesn’t has to call me Johnson.
Yes, yes it does.
Very creepy.
I’ve never heard of a penis called Louis, although Louis is my middle name—don’t go there.
OK, I’ll go somewhere else, back to the OP, and surmise that it may have something to do with the phrase 'Keeping up with the Johnsons".
I don’t think there is a noun that coudn’t mean ‘penis’, in the right context.
The slang word is first recorded in print in a journal from 1863. So it was in use at least by then.
No mention of just where it comes from. Not even a speculation.
I’ll post the question to the American Dialect Society and let them offer some help.
Larry Mudd
You are quite an impressive fount of knowledge on this subject.
I once wrote a short story (honest!) entitled “Magic Johnson’s magic johnson,” wherein the basketball star’s ability on the court derived from his ability to maintain an erection during the action, etc., but when he went and got AIDS, no editor would touch it.
The story. Touch the story. No editor would touch the story.
You’ve got a disgusting mind, you know that?
The local asphalt company here is called Le Grande Johnson. You can’t help but see those big manly trucks go by and get green with envy.
I think a character in a D.H. Lawrence novel reffered to his endowment as Jon Thomas.
Amazing that Smith or Jones never made the ranks.
Mellors, in Lady Chatterly’s Lover. “John Thomas,” to be precise.
What happens when your lady is Jonesing for a Johnson?