A simple AskMetaFilter question (“What does this pin say, and what does it mean?” Answer: Leningrad) inspired a woman with the username posadnitsa (“The posadniki were the medieval mayors of Novgorod. There was one posadnitsa, Marfa Boretskaia, but unlike her I have never incited Tsar Ivan III to invade my hometown…”) to comment: “My host mother in St. Petersburg made annoyed noises whenever anyone brought up Solzhenitsyn; how can anyone take him seriously, she asked, when he actually suggested renaming the beautiful city of St. Petersburg Nevograd?” Needless to say, this caught my attention; some googling turned up an article by Ekaterina Vidyakina on the history of the city’s names that said (my translation; the Russian’s in the extended entry):
The discussion was started off by a letter to the newspaper Smena [‘Change’] by the dissident writer Solzhenitsyn, who at that time  enjoyed greater popularity; he announced that in his opinion the city’s name should not be changed back to “Sankt-Peterburg,” since “it was foisted on [the city] in the 18th century, contrary to the Russian language and Russian consciousness.”
Solzhenitsyn’s letter attracted many replies, in which Leningraders, as well as inhabitants of other cities, proposed their own names for the “nameless” city. Bearing in mind that Russians have never suffered from fantasy [?], one should not be surprised at the variety of names which our good fellow citizens wished to bestow on our city: Petropol, Nevograd, and the like.
So it sounds like it wasn’t Solzhenitsyn himself who proposed it, though it was in response to a letter of his. But I also turned up this sci.lang post by Andrey Frizyuk, who says:
As the name St.Petersburg isn’t particularly poetical, Russian poets (Derzhavin, Pushkin, etc) invented Greeko-Slavic names for the capital: Petropol(is), Petrograd, Nevograd, etc. When the WWI started 90 years ago, there was a discussion if the name should be changed to Petrograd or to Nevograd. The former version proved more popular in official circles, because it was first used by Pushkin in “The Bronze Horseman”. The popular nickname has always been Peter.
Anybody know anything more about this (to my ears stupid-sounding) proposed name?
The original Russian of the excerpt from the article I translated above:
Начало дискуссии положило письмо в газету “Смена” пользовавшегося в то время большей популярностью писателя-диссидента А. Солженицина. В нем автор заявил, что не следует, по его мнению, возвращать городу название “Санкт-Петербург”, так как “оно было в ХVIII веке навязано вопреки русскому языку и русскому сознанию”…
Письмо Солженицина повлекло за собой многочисленные отклики, в которых ленинградцы, да и жители других городов предлагали свои названия для “безымянного” города. Помятуя о том, что русские люди никогда не страдали от фантазии, не стоит удивляться разнообразию наименований, которыми добрые сограждане хотели наградить наш город: Петрополь, Невоград и т.п.