there is word in persian for less than one year (or 6 month in some cases) sheep called "شیشک" [shishak] and there is food called "شیشلیک"[shishlik] originally made by it. but nowadays it's changed and has different recipes .
In the US I have never even seen mutton in the stores. It isn't popular here at all. We have lamb in the stores, but it is expensive. I never buy it.
Mutton is a popular dish in the UK, isn't it?
I just noticed that you are an American. Do you have mutton in the stores where you live? The Muslim grocery stores might have mutton here. I've never checked. The Somali stores have lamb, goat, and camel meat, believe it or not.