Why is Henry Jones Jr. named Indiana?

It seems to be a name he gave himself when he was much younger. No date is given but, as I recall, he was nicknamed Indiana in the TV show The Young Indiana Jones Chronicles (1992-93)

We find out the origin of the name in Indiana Jones and the Last Crusade (1989)

Sallah: Please — what is always with this "Junior"?

Henry Jones Sr.: That's his name: "Henry Jones, Junior."

Indiana Jones: I like "Indiana."

Henry Jones: We named the dog Indiana.

Marcus Brody: May we go home now, please?

Sallah: The dog? You are named after the dog? [laughs]

Indiana: [coldly] I've got a lot of fond memories with that dog

As it turns out the character is, in fact, named after a dog

But it's true. Indiana was the name of an Alaskan malamute George Lucas owned in the '70s.

^Source

According to the wikia page for the dog:

The puppy Indiana was given to young Henry Jones, Jr. by his parents Anna and Henry Sr. while still in the crib at their home in Princeton, New Jersey.

Jones had such affection for the Alaskan Malamute that he considered his best friend, he adopted the name as his own growing up, calling himself "Indiana" by 1905.

The information is derived from Indiana Jones: The Ultimate Guide, a 2008 reference book written by James Luceno, and from "My First Adventure", the first film in The Adventures of Young Indiana Jones.