But, how do you (and do you?) make the difference between an entity that is quoted on the stock exchange and one that is not - the latter, typically, a smaller family-run business, for instance? Can any company be an 'Inc.', then?
In the UK, 'ltd' and 'plc' are not interchangeable at all. Not the same kettle of fish.
Again, I'm not an attorney, but I do not believe there is any way to tell whether a company is privately held or publicly traded from its name alone, with the exception of a "Limited Liaibility Company", or "LLC". LLCs are a form of corporation authorized by Congress in the early to mid 1990s, as I recall. An LLC is the corporate equivalent of a partnership, with the company's income flowing directly through to the shareholders' personal income taxes. (An "S" corporation is a longstanding corporate form that does the same thing, but not as well, apparently, because LLCs -- and LLPs, created at the same time for attorneys and other true partnerships -- are all one sees anymore.)
It's been awhile since I had to review any of this, but when starting a corporation in the U.S., one must signify that it is a corporation, with limited liability, by including one of several terms in its name, but one has the freedom to pick from any of them (LLCs aside). I'm sure these include (or at least, included in 1990) "Company," "Co.," "Incorporated," "Inc.," "Corporation" and "Corp." I believe there was a seventh one, but I no longer recall what it was. Privately held companies "go public" here all the time, and I have never heard of a requirement to change their names as a result (except, of course, that an LLC would have to become a different form of corporation to be publicly held).
The Securities and Exchange Commission imposes many duties on publicly held corporations that are not required of privately held ones, and the public cannot buy shares in a privately held company in any event. So the system seems to work without doing material harm, although I am not familiar with the advantages that might be lost from not being able to identify whether a company is privately held from its name alone.