Hello! I'm Japanese and I'm afraid Mishiki is not a Japanese name, either male or female. It's true It sounds like Japanese but unfortunately it's not a human name. You said you have googled Mishiki and found a lot of Japanese sites,so I did the same. And I found out that there are so many Mishiki as well,but the thing is, it was a site of a famous restaurant called 'Mishiki' and they made up the name. You found a lot of Japanese sites with mishiki and I think it's because many magazines or tourinst information sites have a search engines for restaurants and pubs and shops etc. so that even a stranger can get some information.
Anyway, I read an introduction about the Mishiki restaurant and it said that the meaning of the name is " the colour of the taste". Very attractive name,I suppose.
I hope it could help you somehow. If you have any more quwstion,please ask.