If you really are remixing the level, then people usually are okay with it, but get permission if you can beforehand.
That said: if you download a level, make a few changes but most of the level is completely the same, then its not considered a remix.
A remix is basically, create a new level that is heavily inspired by the original where there are sections you can recognise from the original, but also have completely new sections that were not in the original. If its too close to the original without any new sections, its considered a cover, not a remix, and unless very careful planning and execution was done, most people will think you are trying to rip off the original level and claim it as your own, or just not find enough changes to warrant their time.
So if you can add enough new things to the level and also make it harder, I'm pretty sure everyone will love it and the author of the level will not mind you remixing the level.
As level name, the first option or something similar would work best I'd say, but if you find a really good title that explains the changes, that would also work.