Hello –
Coleus are brightly colored, partial-shade loving plants that come in all kinds of shapes and sizes. This member of the mint family grows well in borders and containers, but will occasionally come under attack from a number of pests and disease. Common coleus problems include:
Pests
โข Mealybugs
โข Aphids
โข Slugs
โข Spider Mites
โข Whitefly
Disease
โข Powdery Mildew
โข Downy Mildew
โข Root Rot
From your description, I think that the moths that you are seeing are actually whiteflies, but they are a sucking insect and don’t typically eat plants. Look for slugs too! I’ve included a couple links below that I hope help.
https://www.planetnatural.com/pest-problem-solver/garden-pests/slug-control/
https://www.planetnatural.com/pest-problem-solver/houseplant-pests/whitefly-control/
Good luck!