The bookends at the psychiatrist's office, where he talks about trying to get his cat down from a tree, is the only time where the name, "Indiana Jones", is mentioned...and it's he, himself, who says it. (Though, in the "London" bookends, Old Vicky/Jane Wyatt does indeed call him, Indy.)
Everyone else calls him, Dr. Jones, Professor Jones, Mr. Jones, Henry, Dad, Grandpa, Gramps, Sir, Mister, Mack, Dude, Old Man, Old-Timer, Old Coot, etc....but never "Indiana".
By the time the '90s rolled around, Indiana Jones had become a forgotten hero.