The stores have been called 7-Eleven since shortly after World War II, and I don’t think I’ve ever seen one of their logos or anything from the parent companies (The Southland Corporation before the 1998 bankruptcy or Ito-Yokado and then Seven and I afterward) that used “7-11” as the trademark. But in any case, if you write that you went down to 7-11, everyone remotely familiar with the store will know whereof you speak, just as well as if you mention going to Wal Mart or Walmart or Wal*mart. Comic book nerds usually remember that Batman is not hyphenated but Spider-man is (oh, wait–I mean “Spider-Man”), but outside of nerd circles or Marvel HQ, nobody gives a hoot if you write “Spiderman” instead.
But those alternate spellings are, strictly speaking, incorrect. It kinda reminds me of that time in the ST:TNG pilot when Dr Crusher mispronounced Data’s name with a short A. When he objected, she asked what the difference was, and he replied, “One is my name. The other is not.” That was intended to set up our empathy for Data as a character rather than as a machine, and iPhones and convenience stores are not, in fact, people, my friends. But we might as well call them by their proper names, I figure, at least up to the point of what we consider reasonable. Consensus agrees upon iPhone (which happens to be formally correct) and dumpster and kleenex (which have become correct through genericism over the decades) and 7-11 (which is incorrect but nobody cares) and Toyota (since TOYOTA is no more NASA than Ford and Honda are). I feel that if you decide to fight this consensus by typing Iphone instead of iPhone, it puts you in the position of having to explain why, every time you encounter a new reader who wonders why you employ this relatively unorthodox spelling of what has become a very common word.
More trouble than it’s worth, in my opinion.