yeah as for dying spandex, it doesn't really work. any fabric that is synthetic will almost never dye, definitely not the color you want. most colored spandex or lycra is heat or sublimate printed, meaning the color is laid on top of the fabric then heated and pressed into it. Like Toacrabman says, sharpie works, although you'll notice it won't be the same color black. it's usually more purple, and can have a sheen to it. I've dealt with this before, and sadly, I don't really know of any way to get that logo off and have it look good :/
So, I just recently had an entire bodysuit be the wrong color for me, and after looking around, and trying multiple methods myself, I just spray painted the entire thing. It changed the consistency of the fabric slightly, but I made sure to do it on a dummy based off myself, and so it still fits fine. And after washing it, it lost a lot of the original stiffness, but didn't lose any of the color (which I was very happy with). You could do something like that though, to cover the logo, and the odd colored area will just blend into the rest of it I would think.