More can be written on such topics, but there are some articles in the "Calendars and timekeeping" AskHistorians wiki page, at "How did the world agree on what year it is?" . The most applicable ones appear to be

AskHistorians Podcast Episode 006, "How did we decide what year it is?" , by the inescapable /u/Algernon_Asimov

"At what point did society begin referring to the year in modern terms (2012 etc)" by Algernon_Asimov again. (I've seen lots of recent calendar and time questions that were originally answered by him. I guess it's ... his time.) He touches on the transition away from consular years, but he doesn't say exactly when it happened.

This is not to discourage discussion. Further questions, data, and debate are welcome.

Dating by consular years continued for as long as Rome had consuls - until 541AD, by our count (after that, the Emperors themselves were the only consuls, so it became useless to date years by the consuls).

In parallel with consular years, and then continuing on after consular years stopped being used, the Romans used a regnal year, similar to places ruled by a monarch: "In the third year of the rule of Emperor so-and-so".

The use of the Anno Domini numbering system was originally more for the benefit of Christian monks than for civil use. It was only adopted gradually by other areas of society, as I previously explained in my comment that /u/scarlet_sage linked to.