I've tried looking for the name of this font, but haven't gotten anywhere.

Thanks for taking the time to read this, and helping out!

P.S. I've seen this font animated and I'm not sure if that's the font itself, or the use of something like After Effects.

Amatic  Suggested by henriavecunk 


Moon Flower  Suggested by ajiee 

This looks like "Amatic" but it has probably been distorted somehow, as you say.

try moon flower