Unless Sak's has Fat Sacks or something real similar registered as one of their trade or product names, how can any reasonable person mistake the name Fat Sacks for Sak's Fifth Ave?
In Hawaii we have a business registration division run by the state. You submit a name you want to use, they run checks to see if anyone has a similar name or one that it might be confused with. If not, they issued you a certificate good for 10 years [renewable]. FWIW, we have Akamai Pest Control, Akamai Painting, Akamai Tree Service, Akamai this and Akamai that. [akamai means smart or intelligent in Hawaiian] We also have Oahu Tree Service and Oahu Crane Service. All these companies are owned by different people.
So yes, if they threatened to sue me in Hawaii, I would tell them go for it. They would not win any award if I had my name registered with the state.