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There are a couple of ways to make your own palette with Inkscape. I'm not familiar with Illustrator, so I don't know how it's done there.
Inkscape natively uses the GIMP palette format (GPL). Here's a tutorial for creating that kind of palette:
https://dl.dropboxusercontent.com/s/ureva7n4uyue6e6/Gimp_Palette_Howto_V0_2.pdf That creates a palette which will be available in all documents, after you install it.
The other kind of palette is a per document palette. It uses an Inkscape feature called Swatches. Here's a tutorial for that kind:
http://goinkscape.com/custom-color-palettes-in-inkscape/As for naming the color (as opposed to the hexcode) I'm not sure. That first tutorial might allow you to name the colors. I'm pretty sure that you can't name them using Swatches, although I could be wrong about that.
If you visit the Home tab on this website, you can see all the best tutorials that I know about, organized somewhat by skill level, and in other ways. There are hundreds of tutorials linked there.