I would add to the other explanations here that it was partly an imitation of a convention of pamphlets produced by satirical writers who would circulate gossip in a literary format.

Not exactly gossip as we would associate it now with magazines and tabloid journalism; highly regarded writers (then, as now) such as Dryden and Pope would write about a character whose name was Lady ------- or Mr -------- and the reader would be expected to fill it in from their knowledge of current events or the whispers of other readers.

I think the intention on the part of writers such as Austen or Mary Shelley, who weren't setting up as satirists, was to imply a sort of knowing reference and emphasise the contemporaneity of their story.

It also saved them from having to specifically mention a town (or as in one case in Austen, a specific military regiment) so that those belonging to it would have no cause to say "Excuse me! that sort of thing doesn't go on in my town/regiment etc" or, possbly more embarrassingly "you are obviously writing about me/Mr George Barker of that town/regiment but just changed the name"