Name Your Poison Day takes place on June 08, 2016. Name Your Poison Day is a day to make a choice. The term "Name Your Poison" is commonly used to suggest that you select among a number of options.
Decision making can be regarded as the mental processes resulting in the selection of a course of action among several alternative scenarios. Every decision making process produces a final choice. The output can be an action or an opinion of choice.
This term has a negative connotation. At the time, it probably referred to some unhappy choice. It is commonly used when asking someone what type of alcoholic drink they want. But, it is also used to refer to any choice of options, good or bad. For example, "Name Your Poison" may refer to selecting an ice cream flavor, a dessert choice, etc...
It may be a simple choice to make, or it might be a difficult decision that requires a lot of thought. It suggests whichever selection was made would be a bad one. Hence, the word “poison” in the phrase.