There are a few place names in the world that end with exclamation marks; for example, Westward Ho! and Saint-Louis-du-Ha! Ha!.
I suppose there are multiple cases here:
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If an ordinary statement ends with such a place name, should it be followed by a full stop/period? "He went to Westward Ho!" or "He went to Westward Ho!." The latter, though ugly, seems strictly correct to me and at least makes it clear that the sentence is not an exclamation, even if the reader has never heard of the place name.
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In an exclamation, should an extra exclamation mark be added? e.g. "He went to Westward Ho!!" Is this, in fact, a restricted situation where multiple exclamation marks could legitimately occur together?
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In a question, I do not see any alternative to simply following the original exclamation mark with a question mark, although it looks like an interrobang: "Did he go to Westward Ho!?"
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Finally, just for completeness and to consider the most unpleasant case, suppose one wanted to express incredulity using an interrobang. Would one then write "He went to Westward Ho!!?"
(Naturally, I suspect that in some of these cases, unless one were quoting, the best advice would be "Recast the sentence".)
Best Answer
The key question here is whether a proper name whose creators included end punctuation for it must be reproduced with that end punctuation in order to be correctly spelled. If the answer to that preliminary question is yes, then we must proceed to the question that the poster asks about how to accommodate the built-in punctuation when introducing context-appropriate punctuation.
The preliminary question came up repeatedly at the consumer technology magazines where I work, thanks to the effervescent marketing personalities who graced the tech landscape with names like Yahoo!, Astound!, and Utter Bullblap!. Our arbitrary, unsympathetic response has been to treat the alphanumeric components of a proper name as integral to the name, and to treat end punctuation as promotional fluff. Goodbye exclamation points, asterisks, virgules, octothorps, and any other symbols attached to the end of a name to attract the unwary eye and sell more units of the product.
To the extent that exotic punctuation is simply a vehicle for promoting sales or market visibility, dutifully reproducing that punctuation amounts to enlisting oneself and one's publication in the promotional effort—hardly a comfortable position for an independent source of information to be in. That awkwardness helps explain why The Economist in February of 2013 adopted a no-exclamation-points-in-product-names style. I applaud that publication for its decision.
The slippery slope of deferring to the preferences of those who invent proper names, whether for commercial products or for towns and other geographical entities, is evident when you consider the annoying reverse-R favored by the Toys "R" Us toy company; does anyone not in marketing feel strongly that people writing about this company should mirror the R to match the backward proper-name style that the company copyrighted? On a more mundane level, would anyone think to include the period in the name of the restaurant chain Carl's Jr. to yield sentences like "Let's go to Carl's Jr.!" "I had lunch at Carl's Jr.." and "Do you want to go to Carl's Jr.?"? It's really quite absurd.