> My suggestion would be to rename a site "disaster indices" and include the waffle index as one index. Even batter (yes) if you add other similar indices, like theme park closures or other.
Is it really necessary to go that far though? I think they just need to stop using the visual mark and make clear that it's unofficial. (But I am very much not a lawyer.) You are allowed to identify a product or company by name so long as it's clear it's not you and trademark law can't be used to stop you (e.g., for a bad review). Maybe the site could be renamed "disaster index based on Waffle House closures" or simply "unofficial feed of Waffle House closures"
Yes you can name a brand name without using their logo.
That's not what the author did here -- he invented a fake logo and chose a domain name and title that include "WaffleHouse." Trademark law is specifically designed to prevent people from creating a fake logo and registering a domain that makes people think it is your own brand. Yes, there is some exception for parodies and criticism, but writing a review / parody sketch is a completely different format than a website that lists information that purports to be official open/closures of your business.
You can't create a product that contains the brand name of another product; I can't invent "Magic Kleenex" or "Better Google," so he similarly can't name something a "Waffle House Index." What he could do is name something "disaster index" or "breakfast restaurant index" where the data happens to be from the waffle house locations.
I think the degree to which the waffle house index is popularized among demographics who make a lot of noise and don't do a lot of spending money at waffle house (an analysis that a BigCo marketing team is more than capable of performing) had something to do with their decision to levy a blank "stop this" rather than something more collaborative.