So why do you call Linking "Overtwist"? I do so to make reading about loopbraiding clearer and to separate two different "Linking" moves from each other. On Masako's website lmbric.net she does not go over Move E, as far as I know it's only talked about in depth in her book and possibly some of her articles*. If you're reading a page describing how to make a particular pattern, you have to pull from context which linking move is being talked about and this can be frustrating to new braiders. To add more complexity, both linking moves are applied to fingerlooping. Now if you're reading the shorthand codes it's easier to tell the difference as they have very different codes.
So let's start with Masako's moves definitions and shorthand codes for the two linking moves. The first linking move is used by a braider working their loops where the loop is given a 360 degree twist (as opposed to closed's 180 twist) and mostly just called linking. The full name is Inside-Through Linking, sometimes noted as IT-L, commonly shorthanded as E. Both closed and linking cause the top and bottom of the braid to interlace and become one braid. The second linking move is used to connect multiple braids together side by side and as far as I can tell only shorthanded as LR-RL and LRxRL and their reversed moves RL-LR/RLxLR. But when talking about braids, it's simply referred to as linking as move E is referred to.
So, without an accompanying shorthand code move by move it can get confusing which is being talked about for new braiders. So to help clarify this when teaching loop braiding, I call move E "Overtwist" but maintain the established shorthand code "E" for continuity. It also helps people visualize what the loop is doing in relation to the open and closed moves. Why didn't you call the other linking move something else, like maybe connector or something? Well, simply because "Linking" is a clear and apt name for what is happening. The LR-RL moves are linking multiple braids together side by side rather than E's top and bottoms.
*Though I have missed things on the first hundred readings a few times on her website and in her book. So if you find it, please let me and us know and I can update this post. I have found her notes on the linking moves between braiders. The fingerloop version, http://www.lmbric.net/IL2/IL2.html. I'll have to scan the site again to see if I can find the handlooping version, but the idea is the same.