Hi,

Can you tell me the name of the plant? Or send me another image that shows the whole plant so that I can identify it?

I see i misspelled Butterfly plant!

I can't be sure from just these photos, but earwigs are common pest of plants, including butterfly bush. 

Can you go out and look at your plants at night or early morning? Grab a flashlight and look for earwigs or other pests on the leaves or hiding in the leaf buds. They will run when they see you coming, so you have to look quickly. If you can see what is eating the plant, we can figure out a preventative solution. 

The damage is only cosmetic. I don't think that it will harm the plant overall. It looks very healthy and vigorous. You can pick off the damaged leaves if you do not like them and the plant will be fine and put out new growth.