Like the other members of the Ultimen, Long Shadow was based on an original character from the old SuperFriends show. In that respect, Long Shadow was a reference/update to Apache Chief, another giant-sized superhero of Native American origin. However, as an artificial human, Long Shadow has no genuine Native American background beyond his implanted memories. Also unlike his SuperFriends counterpart, he requires no phrases to activate his powers. (Apache Chief would shout the magic phrase "Inukchuk" to activate his power and grow to fifty feet tall.)
Notably unlike his teammates, Long Shadow was more cool-headed, humble and didn't let superhero fame go to his head. He still retained his admiration of the heroes of the Justice League, considered them as his role models and continued to desire an alliance with them.
Long Shadow wanted his team to join the Justice League, but the other Ultimen, despite some of whom originally also admired the League, were against it. Unlike the rest of the group, who had been enjoying their newfound fame, wealth, and popularity, Long Shadow earnestly wanted to join the Justice League to help more people and be a better hero. Long Shadow's efforts were constantly rebuffed and mocked by his teammates.
After helping the League, Long Shadow developed somewhat of a crush on Wonder Woman. While the attitudes of the rest of the Ultimen and the Justice League were at odds with each other, Long Shadow's humility and admiration earned a good friendship with Wonder Woman, who became a sort of mentor figure to him.
As the "History" section indicates, the best part is his refreshing personality. He wasn't the stoic or savage member of the Ultimen. In fact, he was the opposite: friendly, helpful, and open about his desire to be a hero.
That doesn't seem like much, but it's surprising how often a Native character is some variation of stoic and savage. It's the 21st century, people. Indians are extroverts and peace lovers like everyone else.
For more on the subject, see Ty Longshadow = Apache Chief? and Apache Chief.