The word is usually spelled "Greenwich", not "Greenwhich". Unless you are thinking of a particular example that you are sure is conventionally spelled "Greenwhich", you should stick with the usual spelling.
There are a number of English place names like this: "Harwich", "Woolwich", "Berwick" and "Warwick" are examples. There are also surnames such as "Beswick" (variously pronounced with or without "w") and "Fenwick" (these, as it happens, are also place names). Offhand I can't think of any examples that aren't proper names (apart from words like "who", "***", "wring", "wrap" etc., but I assume you're not talking about those). That doesn't mean there aren't any, of course.
Edit: Huh? System has asterisked out "w h o r e".