Vader is a member of Sith Order, therefore he has a title of Darth - Darth Vader. But most Imperials address him as Lord Vader. Obi-Wan calls him Darth, but Obi-Wan knows a lot more than others. Was title of Darth known to ordinary Imperials and general public ? If it was, someone more educated could surely connect the dots between this Darth, his Force powers and look, with ancient Sith lords.
Yes, the title of Darth was generally known throughout the Empire, and its meaning was at least somewhat known, but whether Vader was himself a Sith was a matter or rumour rather than fact. The new canon novel Tarkin gives us some insight into the general perception of Darth Vader:
...that had given rise to so many rumours about Vader: that he was a counterpart to the Confederacy's General Grievous the Emperor had been holding in reserve; that he was an augmented human or near-human who had been trained or had trained himself in the ancient dark arts of the Sith; that he was nothing more than a monster fashioned in some clandestine laboratory.
Tarkin's private thoughts later make it clear that he, at least, knew that Vader was indeed a Sith:
Disdain crept into his thoughts. That Vader was a Sith shouldn't factor into the question of authority
Of course, Tarkin was an exceptional individual of great intelligence and education, but it does show that the knowledge of the Darth title was not unusual in the galaxy.
While it is no longer canon, it's worth noting that the title of Darth has quite a rich history in Legends. In that continuity, the Sith were not always as secretive as they have been for the last thousand years; the history of the Republic was littered with various Darths who invaded or attacked it across the millennia. It's also important to note that in Legends, the title was sometimes taken by people with no real connection to the Sith at all (Darth Revan and Darth Malak, who were renegade Jedi rather than true Sith).
All of this gives us a pretty clear idea - Vader was a mysterious figure in the Empire, and while the significance of the Darth title was known, the significance of Vader using it was uncertain.