Each of the ability scores have their own quirks when it comes to negative numbers. 1 in strength is they can't wear clothes because they're so weak, 1 in con is their blood can't clot and they constantly break bones, 1 in intelligence makes you a vegetable. What would a 1 in wisdom be?
Skills related to Wisdom include Perception and Insight, so you could play someone poor at those. Perhaps your character has poor vision, poor hearing, or is extremely gullible and easily deceived. Maybe this leads to poor animal handling abilities, as you don't notice when they are getting aggressive or afraid.
For the headline question: However you like - its your character
With respect to your first sentence ("Each of the ability scores ..."): this is just wrong. There is nothing special about having 1 in any ability score apart from the mechanical effects of having a -5 on skills/attacks related to that ability.