If you need to create a file in CMYK, but where the channels have been renamed to C1, M1, Y1 and K1 you only need to convert from CMYK to Multichannel and rename the channels. No need to make a new spot channel for each CMYK channel and copy the original channel, since they are already spot channels.
(I don't understand exactly why you need to do this, but there are of course many different workflows around the world.)
Now, why does the colors change when you convert from CMYK to Multichannel? This is an important question and a huge subject. I will just scratch the surface.
Basically a CMYK image is just a collection pixels which each have a set of CMYK percentages. Due to an array of physical reasons a certain CMYK color will look different depending on which device you print it on and which paper you choose (among other things). The CMYK percentages are in reality technical instructions to the printing device on which physical raster percentage to use and can't be seen as an objective way to define a color. There is no 100% reliable mathematical way to convert from RGB to CMYK.
The solution to this mess is to use a CMYK color profile which is made by measuring testprints made by a device which complies to a specific standard.
The idea is that if
- your print shop complies to a standard (by certificate or practice),
- you have a good calibrated screen which is in a room with the recommended lighting,
- you convert your RGB images to the appropriate CMYK profile provided by the print shop,
you will get the best possible preview on screen of how the colors will look like on print.
CMYK images can be untagged, without color profile, but there is no way to convert an RGB image to CMYK without using a color profile. When you created the initial CMYK image you have (consciously or not) chosen a specific CMYK color profile. If you just choose Image > Mode > CMYK Color, Photoshop will use the color profile specified in Edit > Color Settings... > Working Spaces > CMYK. This profile is also referred to as Working CMYK.
The colors you see on your screen is how your CMYK image would look if it was printed by a print shop which complies to the CMYK color profile of the image. If the image is untagged it will be shown as if it were Working CMYK. There is no way to see it "without color profile".
Multichannel mode doesn't use color profiles. I believe it is mostly meant for spot colors. The colors you see on screen is Adobe's best bet on how the spot colors will look on print based on their Lab color. Unlike CMYK, the preview is not (directly) based on measurements on physical prints, so it's not completely reliable.
When you convert from CMYK mode to Multichannel mode, the CMYK percentages of each pixel are unchanged. It's the exact same data as before, but the preview of the colors change because you change from color managed CMYK mode to algorithm based Multichannel mode.
This image shows how a neutral gray sRGB color (RGB(128, 128, 128)) converts to different CMYK profiles:
And here is how these same CMYK percentages looks in Multichannel mode:
If the printer you use doesn't use a color profile and wants you to deliver a CMYK file, there is no way you can get an accurate preview on screen. The result might be "something in between".