What is this called? Oak Cabinet Cap?
If I was on a job and somebody was asking for that, they'd call it the little stile on the kick. I've never heard it given a real name. 

I doubt you can buy one off the shelf. You can find a cabinetmaker or woodworker that'll make you one, though. Look for a smaller shop and bring cookies as well as money. If you have the old one, bring it with you.