Transparency is only an issue with spot colors (as the warning states). that's why you won't see the warning when working with CMYK objects.
If you don't want colors to darken due to overprinting, don't set things to overprint. There's no requirement to set CMYK objects to overprint, gradient or not.
The overprinting you are remembering is for when trying to create a gradient from one spot color to another spot color and has nothing to do with CMYK objects.
The swatch part of the question is a bit unclear as to the motivation...
If you used a spot color swatch then its basic structure needs to be changed to separate as process colors and not a spot color.
The name of any process color swatch means nothing for production. It doesn't matter what the swatches are named, they will separate out to CMYK regardless. But the swatch should be set as a process color swatch (which non-spot color swatches are by default). If you started with a spot color swatch then you need to alter the swatch to be a process swatch in the
Swatch Options. Swatches set to spot will generate separate plates when output - you don't want that for process color jobs.