One business name that always threw me when I was younger was the phrase "solicitor". To me, growing up in the US, that was someone who solicited someone for something, usually s*x. When I finally realized that it was another term for a lawyer, it made much more sense.
We have a local car dealership with several makes, Mr. O'Neill. I always laugh because he has websites such as oneillhonda or oneillauto. I was apparently the first person in my family who realized that it could easily be saying One Ill Honda.
We also have a Quick Lube in town, as well as a few bars. There's The Other Place and JJ's Other Place, not in any way connected to each other.
There's a college town I've been to that has a bar called The Library. "Oh, yeah, mom, I was at The Library all night last night..."