I’m talking about modern day countries, if they call it anything other than the 19th century, what is it? I can’t imagine a country like Mexico defining a period of time by a British monarch. So where there even any other names for this period other than Victorian era or 19th century?
In Denmark there is a slight overlap with what is known as the Golden Age (from around the turn of the century to the 1860s). The naming, to some, may seem paradoxical or odd, as the Danish economy and position in the world was taking hit after hit: one of the greatest national treasures (The Golden Horns) was lost, Copenhagen was burnt by the British who did not approve of the concept of neutrality, the fleet was stolen, Norway was lost (to name some highlights); although there was a "victory" against the powerhouse that was Prussia (who soundly beat Denmark in round two in 1864).
But despite these things, literature and arts were flourishing, and the focus changed to how nice and lovely a place Denmark was.
But if you ask what people in Denmark would call the period now, the answer would most likely just be the 19th century. The Victorian Era is only used in relation to the British, and even then it's rare
In French history you often call eras by the government of the time, such as Third Republic, July Monarchy, Bourbon Restoration, etc. I would imagine that other countries are similar and follow the political situation. In a small country, the era may have to do with the surrounding area or in a colony/new world nation the era may follow the colonizing country's history (Unless there was an important local situation that is worth recognizing as an era). These labels are used with purpose: ie. can you claim that the situation you speak of remains the same for the reign of a particular king or is it more specific (in which case you might refer to a smaller "era" within a larger one, like Belle époque), or is it less specific (in which case the century or particular half-century may suffice).