Flo (spinoff of Alice): Flo’s Yellow Rose
Twin Peaks: One Eyed Jack’s
The Peach Pit in Beverly Hills 90210
Gibbs & Co. regularly patronize an unnamed diner in NCIS.
Known as Orcini’s under the previous proprieter.
Also Reggie’s. And there was that Chinese restaurant…
The *Friends *all hung out at Central Perk
Speaking of which, Phoebe’s twin, Ursula, worked at Riff’s, a place frequented by Paul and Jamie on Mad About You
*Laverne and Shirley *- The Pizza Bowl
The Cheesecake Factory on Big Bang Theory.
There was also the Chinese restaurant owned and/or managed by the same guy who was at the Chinese restaurant in Seinfeld (James Hong).
Alas, it doesn’t like like the Soup Nazi’s place was ever specifically named. 
The crossroads inn on Game of Thrones.
The Gaslight Cafe is where Midge gets her start as a comic at an open mic night in The Marvelous Mrs. Maisel.
Parks and Recreation had *JJ’s Diner *and *The Snakehole Lounge *(a great name for a dive bar) as well as several others.
But the champion for restaurant names has to be The Good Place, which may number in the hundred’s by now. Some of my favorites:
Ponzu Scheme
Sushi and the Banshees
Knish from a Rose
Heck, yes!
This article references a massive list of pun-based restaurant names which one of the writers came up with for a single episode. And, even then, the writer notes that it’s an abridged version of the list. 
The Good Place resturants fail one of the conditions from the OP: mentioned a few times.
I seem to recall that, on one or two occasions, various people from WKRP in Cincinnati went to a bar called Snooky’s.
Ah, thought of a few more. Going on memory here, so I may have a few details wrong:
Hotel: The bar was the Cavalier Bar, and the dining room was the Carlyle Room.
The Love Boat: I think that the dining room (where the Captain’s table was) was called the Coral Dining Room. There was also a bar–well, there were many bars on the ship, but this one was inside, not outside by the pool–called the Pirate’s Cove.
Square Pegs: When not in school, the kids hung out at a place they called “The Grease,” although its real name was, IIRC, Acropolis Luncheonette.
And the Bada Bing strip club.
My favorite from The Simpsons:
Professor PJ Cornucopia’s Fantastic Foodmagorium and Great American Steakery.
Futurama: O’Zorgnax’s Pub, Elzar’s, Fishy Joe’s, Panucci’s Pizza
The Gem and the Bella Union on Deadwood.
Los Pollos Hermanos, The Dog House, and The Grove on Breaking Bad.
Babbette’s Supper Club and the Onyx Club on Boardwalk Empire.
When they weren’t committing murder, treason or torture, Olivia Pope and the gang on Scandal liked fast food from “Getty’s Burgers”. Well, Olivia more liked wine and popcorn than burgers, but everyone else liked their food.
Bueno Nacho – *Kim Possible *
[del]Shitty[/del] City Wok – *South Park *
We can make this a game. The name of this restaurant was simply “Pierre’s”.