As long as I remember the name is Henry Walton Jones Jr, but I have never read why the Indiana nickname. Is there any background info of this?
This final clip from The Last Crusade says it all.
I got a lot of fond memories of that dog.
At the beginning of the movie we see Indiana Jones as a teenager, and his fellow scout calls him 'Indiana.' So perhaps as an assumed only child with a strict father his best friend was his dog Indiana, and when it passed away, he decided the best way to remember it was to take the name for himself.
Indiana Jones likes dates.
Maybe the Jones family wasn't actually from Utah; perhaps they moved around as Henry Sr. took one professorship after another. It's plausible that they moved there from Indiana, and Jr. was assigned the nickname as a matter of group convenience.
"Henry?! Naw, we already got Big Henry and Little Hank in the club. Where'd'ja come from?"
"Ok, Indiana, let me show you around the neigborhood."