In an Instagram post, the chef confirmed the new name, adding that it would form part of The Pony Restaurant Group.
The group will also encompass a new bistro that's set to open in Bristol in May; and The Queens pub, also in Chew Magna, which is expected to launch in the coming months.
It was reported back in January that the Michelin-starred Pony and Trap gastropub, which Josh and his sister Holly Eggleton took over back in 2006, had closed permanently and was to reopen as a community interest space that offers baking, foraging and fermentation courses.
Its gardens will host volunteering opportunities, with those involved in the schemes given lunch and a veg box in return.
Meanwhile, a set number of people interested in but unable to afford what has been described by Josh as 'some really refined gastronomy' will also be invited to eat for free at one of three weekly communal dinners hosted by the new venue.
Describing the concept earlier this year, Josh told The Guardian: "It’s a Robin Hood thing. We’re going to charge the rich and give it back to people who need it. That’s the way the world should work: redistribution of wealth.
“Dining won’t be a simple transaction of ‘pay us loads of money and we bend over backwards’.
“That’s the old way. I want my staff to enjoy it. It’ll be like coming to my house.
"The kitchen will be integrated into the restaurant and people can walk in and watch me. I’m not coming to the table to dress the plate.
"Pick your plate up and watch me take apart this turbot. Invest in me. I’ll invest in you.”
Late last year Josh and Holly announced that they had also taken on a new site on North Street in Bristol's Bedminster district, which will be known as The Pony North Street and is described as 'a modern-British bistro'.
The pair are also planning to launch The Queen’s pub in Chew Magna this year, which will serve a menu of ' sharp pub grub and Sunday roasts'.
It is understood the opening of The Queen was in the pipeline prior to the pandemic, and that the site will eventually also have capacity for four bedrooms.
Josh also runs award-winning fish and chip restaurant Salt and Malt and the vegetable-centric Root at the Cargo development in Wapping Wharf; The Kensington Arms in Redland; and Yurt Lush in Redcliffe.
In July last year, following the lifting of nationwide Coronavirus lockdown restrictions, he also joined forces with other Bristol-based chefs and restaurateurs to launch Breaking Bread, a pop-up restaurant space at the bottom of Clifton Downs that was created to give a boost to the city’s hospitality sector.
A note on The Pony and Trap website says there are currently plans in the works to bring back the space this summer too.