The precise location that Ponce de Leon landed on is debated. It may have been in what is now St. Augustine. Other possibilities are further south and include what is now called Ponce de Leon Inlet, or Melbourne Beach.
Yes, Juan Ponce de Leon was the first European Explorer to discover Florida on April 2, 1513 so he named it. Historians believe he first named it "Pascua de Florida" meaning 'feast of flowers' or "La Florida" meaning 'flowery'.
He discovered Florida. He was looking for the fountain of youth. Actually, Ponce De Leon wanted to get revenge because he got fired from being king of Spain and got replaced by Christopher Columbus' son so he went north and found Florida.