The Boreal Forest has two other common names: the snow forest, and, taiga. These three terms can be used interchangeably, but Boreal or taiga are more often used in formal/academic contexts.
'Taiga' is Russian in origin, meaning 'land of little sticks'. 'Boreal' originates from the Greek for 'northern', and usually refers to the climatic zone south of the Arctic. Aside from the forest, the term (in the Latin form) is also used to describe the Aurora Borealis (northern lights).
Unlike the Greek and Russian terms above, 'snow forest' is a more colloquial term for the forest. The term comes about as a literal description of the evergreen forest with long winters and high precipitation.
There are further names used for the forest: the 'Coniferous forest' is another name used in an online context, but not an academic sense.