Use old fashioned oats: Old fashioned oats soften well overnight and give the best texture. Quick oats can get too soft, and steel cut oats will not soften the same way.
Use pumpkin puree: Make sure you are using plain pumpkin puree, not pumpkin pie filling, which already has added sugar and spices.
Stir before serving: The oats will thicken as they chill, so give them a good stir before eating.
Adjust the thickness: If the oats are too thick after chilling, stir in a splash of milk until they reach the texture you like.
Add toppings right before serving: Nuts, seeds, chocolate chips, or extra cinnamon are best added at the end so they keep their texture.