The name of the shop is 'Szymon's Famous Coffees' and it's where people working at Lucky7Insurance get their beverages from. The name of the shop was already readable on the cups in previous episodes.
And yeah, I'd say the 'z' is a clear reference to the zig-zaggy floor pattern of the waiting room, not unlike the Z on Tracey and Sam's cups.
Also the Szymon name kinda reminds me of Simon the Magician, but that's just speculation.
Ah! Damn, I need a better TV!
Ah, with a z is the Polish version of Simon.
I'm assuming the s at the end just means that it belongs to the Szymon family, like, "Szymon's," but I don't remember if it had an apostrophe or not.
Yes!!! A connection to Inland Empire, no doubt.
Ah so, Mike was just saving Dougie from assassination basically from the Mitchems.
Or, as mentioned in another thread, Coop is building an army. So it seems, with the help of Mike.
I am from Poland, it is a popular name here. I was surprised when I noticed it but on the other hand Lynch worked in Poland and with Poles so it shouldn't be a surprise.
Also, as someone on my Facebook group spotted, the circle with rays coming out is the same as on the Big Ed's Gas sign. I'm too lazy to post images but they're similar enough that it's probably deliberate. Not sure whether the same symbol's been used elsewhere.
Edit: on closer inspection, they only look the same in a small image. If you look closer the coffee shop logo is clearly a pie. So it's probably a coincidental similarity.