I can't comment on Russian versions of the names, but linguistically, Ivan is John. It's a Biblical name. In Italian, that's Giovanni; in German, Johann; in Spanish, Juan; in Portuguese, Joao; in French, Jean, etc.
I don't think anyone associates the name Ivan with Russia because it's widespread even outside Slavic countries. Typical Russian name, when a movie director wants to be sure, is Sergey (Sergej).
My name, Ivo, is one of the variations of the name Ivan. In South Slavic languages, we have Ivan, Ivica and Ivo as male names. English equivalents would be John, Johnny and Joe. So, I'm Joe.