....then why the name Wagner?
"Wagner" was Utkin's nom de guerre. Then, when the organization expanded, his name began to be used by journalists to describe the whole operation. After journalists began using the name, the people inside Wagner decided to adopt the name for themselves.
Utkin was like you, BB :) Members of the Wagner Group have said that he was a Rodnover, a believer in the Slavic native faith. A Pagan, basically!
In any case, whether Utkin was a Pagan, a Neo-Nazi, a fan of Wagner's operas, or an admirer of Hitler - is not important. Prigozhin ultimately was the head of the organization (once it left its embryonic stages), and even he received his orders from the GRU. One Pagan/Neo-Nazi commander, does not make a Nazi organization.
Wagner had Jews, Koreans, Buryats, Tuvans, Russians, Ukrainians, Congolese, Syrians, Azeris, Chechens, Cubans, Kyrgyz, Belarusians, and Kazakhs serving in it. The main motivation was not "to keep Russia white", but to make fat stacks of cash while living outside all norms of society. Furthering Russia's interests was merely a bonus.