This volume, published by the Federal Writer's Project, provides a paragraph on President's Island. Read it here. Either I have grossly underestimated the size of the island, or this publication grossly overestimated it, but the stated size in this text is 32,000 acres.
The article also states that the island was named after Andrew Jackson, who for a time owned land there. Most people I believe reject this explanation for the island's name.
See also History of the City of Memphis, Tennessee. Here, the editor likewise writes that the island is named after Andrew Jackson. He dates the naming to 1820.