Do I need something under my head during a Feldenkrais Awareness Through Movement® (ATM®) lesson?
Maybe. You can reference this illustration to help you decide if you need something under your head and how much:

Can I use my regular pillow?
I do not recommend it because most regular pillows are too squishy. A firm but still comfortable surface that allows for movement is ideal for Feldenkrais lessons. Try one of the suggested head supports below first. If a pillow is the only head support that is comfortable for you, use your pillow. When you feel ready, you can experiment using different head supports.
What do you suggest for head support?

I prefer foam gardening kneeling pads. Comes in many sizes and thicknesses. Drape a towel on top if you want.

Paperback books and a towel can work well. Paper back books for firmness. Towel for more cushion/comfort.