JAMA and the Archives Journals capitalize trade names according to the spelling of the legal trademarks, even if they begin with a lowercase letter and contain a capitalized letter.
She sold her collection of vintage hats on eBay.
Data were processed in the field on iBook computers (Apple, Cupertino, California).
Avoid starting a sentence with one of these trade names. It is almost always preferable to reword the sentence so that it begins with a word that takes an initial capital letter, while retaining the preferred spelling of the trade name.