Viper is named Viper because of its striking speed similar to the animal, long swords referencing its deadly teeth, its behavior of ambushing prey and attacking from dead angles and its lethality.
Poison is a possibility but not a garantee. We have enough to be satisfied with all the Viper references.

Is Captain Falcon able to fly?
Is Batman able to use echolocation?
Is Flash able to produce a Flash?
Is Solid Snake able to bite and poison its ennemies?

If those characters have no problem being named after animal or natural events, why would it be a problem for Viper?