Yes, Mr. Jones does own the Manor Farm at the beginning of the novel; however, the power dynamic changes from the humans to the pigs. Cleverly the pigs tell of Animalism and create the appearance that ALL the animals own Animal Farm. In reality the pigs (Snowball and Napoleon) own the farm. Near the end of the novel the ownership changes once again into the hands of the dictator, Napoleon. In Chapter 10, Napoleon is dealing with the humans and decides the name should restore to its rightful title--Manor Farm. Animal Farm is no more!
Mr. Jones is the owner and operator of Manor Farm at the beginning of Animal Farm. In Chapter 2 Mr. Jones goes into town and has too much to drink and forgets to take care of the animals - not feeding them, or milking the cows. In desperation the animals break into the barn and eventually drive Mr. Jones, his wife and the workers off the farm. At that point the animals now run Manor Farm, whose name they change to Animal Farm.
Mr. Jones was the owner of Manor farm. He represented Czar the secon d. They both were really powerful, however were ineffective. Towards the end however, Napolean becomes the owner of Manor Farm as he changes the name back to Manor Farm. It was called animal farm for most of the book, (hence the title of the book) but later Napolean realized that it should be called Manor Farm as it was mainly run by the pigs, (mainly Napolean, who was like a dictator) who assumed they were humans and started behaving like them. Since they thought they were humans, they found it pretty pointless to call it 'Animal Farm'