This question and similar ones about BC/AD dating come up frequently, and we have a lot of answers in the FAQ about them:

How confident are we that the year is actually and exactly 2016? Is it possible that at some point in the last 2000 years there were any significant timekeeping mistakes? and Did people in the Middle Ages call the year "one thousand and one" or "ten oh one"? by /u/sunagainstgold

At what point did society begin referring to the year in modern terms (2012 etc)? by /u/Algernon_Asimov

Was the millennium from 999-1000 ad marked in any special way? by /u/savvysioux

Did people in 999 AD celebrate the new millennium? Were there any doomsday predictions similar to Y2K? by /u/haimoofauxerre

In brief, the answer is very few - some highly-educated Christians in western Latin Europe would have known about the dating system devised by Dionysius Exiguus, but even then, they tended to use regnal dates instead of "anno domini" dates. For example a document issued by Robert II of France would be dated "in the fourth year" of his reign; Pope Sylvester II would refer to the "second year" of his reign.

Greek-speaking Christians would use the "anno mundi" calendar, dated from the creation of the universe, which they established as 5509 BC. The year 1000 AD was Anno Mundi 6508. On the Islamic calendar it was 390 years since Muhammad's migration to Medina; and on the Jewish calendar, also dated from the creation of the universe but with a different calculation than the ones the Greeks used, it was the year 4760.