Origins of the name
If you type in "Soldier Blue" in any search engine, you'll find it's the title of a 1970 western directed by Ralph Nelson. Where's the connection, you might ask? I have no idea what Takemiya Keiko had in mind, but maybe it was a complete coincidence.
If his name had to do with the movie, it probably has something to do with the hate and fear two groups of people had for each other. The movie fictionalizes the Sand Creek massacre in 1864, and appears to have provided some "reason" for it. As America was still in Vietnam, the movie added more violence to the already existing war.
The movie itself was very graphic in its depiction of violence. And as movies of that era goes, there was nudity, too.
I don't actually know why the movie was named so, probably because I am no fan of westerns, but our Soldier Blue, from Terra e, might have gotten his name from the film because he is a part of a war between two groups of people. He doesn't support violence in any way though, and spends much of his time fighting to find their home, the true earth.
Another quite obvious reason for his name is because he is a Type Blue Mu, a classification given to him by humans for his level of ability. The soldier part was probably because of his rank within the Mu people.
Lastly, Soldier Blue is also the name of a drama CD from the Bubblegum Crisis series, which is suppose to bridge the story between Bubblegum Crisis and Bubblegum Crash. But as the drama CD was made in 1991, it really doesn't have much hold over our Soldier Blue, who was created in 1977.