The company's browser will still be named Edge and should retain the current look and feel. The decision to switch was motivated primarily by compatibility problems: Web developers increasingly test their pages exclusively in Chrome, which has put Edge at a significant disadvantage. Microsoft's engineers have found that problematic pages could often be made Edge compatible with only very minor alterations, but because Web devs aren't using Edge at all, they don't even know that they need to change anything.
The story is, however, a little more complex. The initial version of Edge that shipped with the first version of Windows 10 was rudimentary, to say the least. It was the bare bones of a browser, but with extremely limited capabilities around things like tab management and password management, no extension model, and generally lacking in the creature comforts that represent the difference between a bare rendering engine and an actual usable browser. It also had stability issues; crashes and hangs were not uncommon.