The Japanese spelling of Yoshi is Yosshii ヨッシー
I couldn't find any information regarding the origin of this name.
Is it a Japanese name ? Does it mean anything ?
It's written in katakana which suggests to me that it is not a Japanese name and has no meaning.
According to ヨッシー in Japanese Wikipedia:
「ヨッシー」という命名は、任天堂社員のあだ名に由来。
(Translation: The name ヨッシー derived from a nickname of a Nintendo employee.)
So ヨッシー was the nickname of a real person in Nintendo.
Is this a common nickname in Japanese? Yes. Many Japanese surnames have よし (Usually 吉 in kanji, for example you may know this 吉田 and this 吉田), and ヨッシー is a reasonable nickname for someone whose surname contains よし. Also note that a nickname can be written in katakana regardless of the etymology.
