What's this haircut called? and can I do it myself at home?

It is the same length all over his head and then tapered close to the ears and at the back. Likely if you have a shaver with a guide, it would be guide #3 or #4. Of course, you'll want to use the bare blade to clean your neck and shape the hair in the back and over your ears. I used to cut my husband's hair this way.