Can’t recall the location, but I once passed a doggie daycare place called Yappy Trails.
I can’t believe no one has mentioned that 50’s classic, The Dew Drop Inn.
When Japanese small cars were first popular, Palo Alto had a repair shop called The Japanese Beetle.
Also in the bay area, The Bay City Screw and Bolt Company.
Never been there, but a bar in Alaska halfway between Fairbanks and somewhere else is called Skinny Dick’s Halfway Inn.
Long gone, a campus soup & salad place at Bowling Green State University was called the Bowl and Greenery.
There’s another (or used to be) The Office bar in Santa Monica, CA
I remember a dog groomer’s in Columbus, OH called The Barking Lot.
I always thought I’d like to add my own strip club to our collection around the local army base and call it The Fox Hole. In fact, it’s fun to think of strip club names.
Then there were the former side-by-side bars Pussy Galore and Pussy Alive. As I’ve related before, I still have memories of a friend and I walking through the Patpong red-light area, and Pussy Galore was packed while Pussy Alive was empty. The girls in Pussy Alive tried to entice us in, and my friend said: “Sorry, but the Pussy looks more Galore in there than it does Alive in here.” 
We’ve got a couple of those. There’s The Office, and there’s The Other Office. he joke is you can truthfully tell your wife on the phone: “I’m at The Office, honey.”
John’s Steel Erections. Their moto is, “We get it up.”
There’s allegedly a sandwich shop in Scotland called:
Sarnie Schwarzenegger
Slogan: “You’ll be back”
nitpick: It’s “Fat Girls BBQ and Cafe.” A friend and I made the hour-long trek based on the name alone, and it does indeed have excellent BBQ.
I prefer the unintentionally funny names and the deadpan ambiguities to the elaborate puns.
A local tool business whose sign (small and crudely painted) I enjoy seeing:
ALL DIE, INC.
(6009 Manchester Ave. in St Louis.)
The Bush Company ought to be called “Gynecology Lessons”: there’s very little actual “bush” to be seen.
There used to be a place down on east 5th Ave during the oil boom called Twin Peaks Bra Shop. I believe it was a front for call girls.
My current favorite here in Portland is the Chinese restaurant Hung Far Low, which has apparently been an institution here since the 1920s.
A new one has been brought to my attention. This is doubly good since it’s Thailand. Down South in Phuket is a serviced apartment complex called … Sleep with Me. Mentioned in the last paragraph of this story. 
One of the best steakhouses in Northern Virginia is called Ray’s the Steaks. Yes, the owner’s name is Ray.
Master Bait & Tackle (i also love their website name, www.masterbaitonline.com.
Minneapolis liquor stores G-Will Liquors.
A good friend of mine is a partner in a Vietmanese restaurant named Pho Sure.
My favorite Chinese restaurant was called Foo King Chinese ( or so I thought for years) then they fixed the sign and it turned out they were really called Food King Chinese. There used to be a very upscale Chinese restaurant in NYC in the '80’s called Dewey Wong.
I always liked Atlanta’s late Boston Sea Party eatery.
In Raleigh, NC during the 70’s (at least) there were two businesses I just loved:
Fat Daddy’s Record Shop & Rib Crib
RB Supreme Broasted Chicken and Concrete Contractor
RB’s had an account with the bank I worked for. That was really the name of the business as registered with the state and city. And yes, they were a concrete contractor AND they sold this weird (but good) chicken that was “broasted” in some kind of pressure cooker thingy. I’d go down there and get Mae to make me up some of that tasty chicken while I watched the guys fill the concrete trucks. Swear to god.
Their deposits always had concrete dust and chicken grease on the money.
Many of them around, but I’ve always gotten a chuckle out of the King Of Clubs. Needless to say, the ones I’ve seen are anything but.
There’s a place on Front St in Toronto called C’est What? 
There’s a popular Thai band called Big Ass.
I have no idea why, but for some reason I get their catalog at work. I’ve come to be able to recognize their fans (or at least the style). I like noticing them and pointing it out to a friend
Me: Hey, that’s a big ass fan (purposely setting the joke up)
Friend: Umm, yeah, I guess it’s pretty big. (the line I was hoping for)
Me: No, I mean it’s the, nevermind, not that funny anymore. (sigh, don’t know why I keep doing it)