A note; whether 柴犬 is commonly read しばいぬ or しばけん varies based on region.

Apparently, the correct reading is しばいぬ, and 柴犬 are listed as such as 天然記念物 (natural monuments) and have been since the 1930's. It's also one of those cases where the 訓読み for both characters is used, hence 柴 ->　しば　and 犬 ->　いぬ.

However, living in Kyushu, I've yet to meet anyone who refers to shiba as しばけん (and, actually, I can't remember ever hearing it on TV either). I was corrected frequently when I first got here and still occasionally "slip up" now; each time I've explained that, in English, we call them Shiba Inu and everyone's been like "へー, someone who can't read kanji transferred it to English that way."

A true 柴犬 fan knows both readings, and which one they use probably varies greatly on region, what they've been saying since they were younger, and which one they prefer, but it was interesting to me to find out that, after years of thinking we were saying it wrong in English, it was a matter of kanji being weird and/or regional differences.

There's a similar phenomenon surrounding 秋田犬; the correct reading is あきたいぬ, but many people refer to the dogs as あきたけん.

Just a tidbit of information that someone concerned with 柴犬 might find interesting.