Which is the correct phrase?
- Name of colours
- Names of colour
- Names of colours
I'm not a native speaker, but I strongly believe 3. is the correct phrase.
This is so because there is more than one name, and there is more than one colour, so both "name" and "colour" should be plural.
"Names of X", when X is singular, could be correct only if X was a single, unique, object / animal / person and if it had more than one name.
Upvoted A. Darwin, but just to add:
If you're talking about one color, use the singular. "What is the name of the color of that piece of paper?"
If you're talking about many colors, use the plural. "What are the names of the colors in that painting?"
"Names of color" would make sense if there were many names for one color. Like, "I call this 'red', but my wife has many names for this color: red, burgundy, crimson, cherry, etc." Or if you were talking about names in multiple languages: the French call it "rouge" and the Germans call it "rot" and so on.
"Name of colors" indicates there is one name for many colors. Perhaps if you were talking about many shades of a color, you could say "The name of all these colors is 'red'." Or if you were talking about some set of colors. "The name of the colors on this palette is 'palette 7'." Though we'd be more likely to say that's the name of the palette than of the colors.
I would use
Hope that helps.