I might be wrong, but I thought "Yasha" meant something like, forest child. I will double check, and if I'm wrong, I'll post the correct informantion.
Edit: Here's some information I found.
Inuyasha FAQ
Question:What does the name "Inuyasha" mean in Japanese?
Answer:
Inuyasha in Japanese translates to "Dog-Demon" but many people are confused with a different version that means it's a female dog demon which is wrong.
Posted by Naraku on Sunday December 21 ,2003
Inu means "dog" yasha means "demon"
Posted by zach on Monday December 22 ,2003
And here is the direct link to the website where I found it.
www.inuyashaworld.com/faq_answer.cfm?ID=21
Hope this helps.