When was the last volcanic eruption in the world? what is the name of the volcano?

Well, to be honest, there is no official way to find out which volcano erupted recently as scientists don't have that type of equipment ready or in use at all; also there is no official way [ ... ] because there are always eruptions occurring.

If you want the most known, "Calbuco" is your answer. It erupted in 2014 and it is found in Chile.