The colors most certainly exist without the name. You may have described the fruit as being a weird shade of red, but if someone held up something red and said "so it was this color" you'd say no. Conversely if someone held up something that was actually orange colored, you'd say "yeah it was that color."

Similarly, you may have no idea what the name is for the color of a Tangerine, but you know what that color is. You might describe it as a dark orange. If I say the name for it is coquelicot, you can look up coquelicot and see if it matches the color you picture in your mind.

The name for the color doesn’t exist before the name. But, you can distinguish all sorts of colors you don’t know the name for. Look at a smooth color wheel or a wall of paint swatches.