I don't know why they would call a gardner the person in charge of stores in a castle.
I've found evidence that Sir Osbern Gardner, the Knight, was the first bearer of the surname. He was the son of Sir Thomas de Gardinis, son of Roger de Gardino. I believe that the Gardner surname derived from the French name Des Jardin, which means "of the garden" in French. Their was a knight named William Des Jardin who invaded during the Norman Conquest. The name de Gardinis means "of the garden" in Latin.
However, the word "Gar" in old English means weapon any way you look at it. I've seen evidence of the name Gairdner, and a gairden was a fortress, meaning the Gardner was a warrior in the Scotch - Irish language of Gaelic. The name Gardyner means "clashing of arms".
I personally believe that the Gardners were Vikings who invaded France, became Normans, invaded England where the name fully developed.
I recently found out my relatives' DNA had 1 hit in the Isle of Man and 25 hits in England.