She really ought to appeal. It's expensive, yes, and it would mean she's carrying the load for the benefit of a lot of other people more than for herself.
The case concerns a coffee shop owned and operated in Astoria by Samantha Buck, specifically what she chose to call it. One of the matters of business regulation in this country is that you can't call your business absolutely anything you want; if it is highly misleading, or if it confuses customers and others with another business, then some limitations do come into play. Most of us find these generally reasonable.
One of the usual principles of long standing at play, though, is that - as long as you make reasonable effort to avoid impinging on someone else - you can use your own name in the business. Hence, in this case, a coffee shop called "Sambuck's." Ooperated, on site, by one Sam Buck.
You see where this is headed: Starbuck's, notwithstanding that it has no coffee shop of its own in Astoria, took umbrage and went to court. Sam Buck's use of her own name was dilution of the corporate image-building, it contended. (They obviously couldn't have used the confusion argument: Look at the logo.) Whether it prevailed in federal court because it had the larger share of the law or the larger portion of paid legal counsel on its side, the result was as you might expect: By court order, Sam Buck can no longer use her own name for her business.
She should start a legal defense fund, with controbutions sought from all the other small business owners who may well one day run similarly afoul of a behemoth.