Historical Context in The Lady with the Pet Dog
In Russian, and many other Slavic cultures, it is common to address someone by their first name and their patronymic, an equivalent to the American middle name, but derived from the father's first name--in Anna's case, Sergey. Interestingly, she does not tell Gurov her last name, which perhaps has some significance on why she has decided to meet with Gurov even though she is married.
Chekhov's omission of the name of Anna Sergeyevna's hometown is characteristic of Russian censorship. Russian authors had to submit their work to a the censors before it could be published, and often the names of certain towns, officials, or other sensitive matter was redacted.
Literally translated from the Russian, this means "she never used the 'hard sign' in letters." The hard sign (ъ) is a feature of the Russian alphabet. This was characteristic of a progressive intellectual at the time and anticipated the reform of the Russian alphabet.
One of the most striking features of the story is that Chekhov ends it with an air of uncertainty. Such endings weren't typical of Russian literature at the time, and Chekhov seems to imply that life, unlike a story, does not conform to neat patterns; rather, it continues in a way that defies human control. This kind of ending (a "zero ending") has since become become a staple of the modern short story.