It was originally "Avatar of Osiris", but still produced "God Slifer Token". I changed it nearly two years ago, probably because I thought the names Osiris and Obelisk were too similar. But I'll stick with Slifer, because I happen to like the sound of the name (note that I don't know if it's an utterly bad change of name).
There are times I'll hark back to the Japanese names (e.g. "Ancient Gear"), and there are times I'll hark to the English. Times of harking to the Japanese appear to be in the past, because I used to read the Japanese spoilers more fervently in the past, and was more familiar with the original names. But rest assured that if Cyber Valley becomes a Deck Master, it'll be based around the word "Vary". I do know that much.
And, actually, I do do a bit of harking with the three Wicked Gods (Avatar, Eraser and Dreadroot), which you'll see when I make the next update. I think I've got about 30 new Deck Masters to put up. Frankly, I need to update, considering the last update was in November, and that since then my claim of "over a third of monsters have Abilities" has become wrong. Not to mention the last two sets (and all recent promos) are not represented at all... yet.