I would call those Christian names, as opposed to Biblical names. And I quarrel with your classification. For common English names, I would split them into Latinate, Hellenic, Germanic, Hebraic, Celtic, African, and others. I bet you could catch 90% of used names in the non-other categories. Almost certainly 90% of names used with significant frequency.
And there's a pretty big chunk of Germanic names, still. Edward, Henry, Eric, even Richard. :) Celtic is surprisingly prevalent, with Kevin, Jennifer, Logan (though the Scots first used it for people), and it has a lot of importance of adding name variants as they passed through Celtic languages from other places, like Caitlin from Katherine, Sean and Ian from John, Liam from William, and many others.
Edit: I guess I'll drop my favorite name etymology trivia bit here: Henry is a name for something you probably wouldn't expect. Henry, Henri (French), Heinrich (probably Frankish? Now German), Haimirich (old German, from home-rich, rich as in regal), and then back up through Latin Emericus, Amerigo in Italian, and as Amerigo Vespucci signed his name in Latin, Americus, which someone feminized to name America.