Grocery store names can be predictable - stuff like Sav-Mor, Fresh Mart, Shop 'n' Save, and so on. There's also family names, silly names like Piggy Wiggly ... you get the idea. You can tell a lot from a store name; something like "Green Harvest" is going to be a foo-foo organic store, while "Valu Mart" will look like something out of the 1960s.
In a similar vein as Piggy Wiggly, there could be ...
Crazy savings every day
✡ Your neighborhood Kosher grocer in the Tri-State region ✡
☪ Your neighborhood Halal grocer in the Tri-State region ☪
Head to the Southwest, and you'll find ...
Super Cucaraceria #1 y #2 - Albuquerque
Super Cucarachceria #3 y #4 - El Paso
Super Cucaraceria #5 - Las Cruces
Super Cucaraceria #6 - Tucson
Mas Super Cucaraceria #7 - Houston
In Canada, the name doesn't matter, as long as there's no apostrophe so the Quebec language police stays happy, and a maple leaf somewhere in the logo for the other provinces.