I have an RGB PSD document with 300 dpi resolution. Basically I designed it to print as my business card. When converting this from RGB to CMYK, my original colors are changing. Is there any way to keep the colors intact so CMYK looks exactly the same as RGB?
No, you can't expect RGB colors to translate exactly to CMYK for printing. This is a fundamental, simple fact. You can't fight physics -- the physical qualities of light vs. ink on paper.
You can't use RGB for printing for the same reason you can't light up a room by holding up a photo of a torch.
A torch is fire, giving off light. A photograph or magazine is paper with ink on it, which can only reflect the light that shines on it. A monitor is fire compared to printed materials.
Monitors make colors with light. Light can be any intensity. Ink is made of solid physical colors from things like rocks, which are ground up and put in a medium like oil or latex. You spread ink on paper and it's never going to be as bright as a color on a monitor.
Offset printing presses use four specific ink colors -- CYMK. When they are mixed together, they can produce many shades, but not nearly the type of shades -- such as electric green, safety orange, deep blues, and many other shades and intensities -- that can be produced by a monitor, or by special chemical mixtures (having nothing to do with CMYK) that create specialized inks/paints.
By changing color mode you essentially change colors.
RGB and CMYK are entirely different color spaces, and can't even reproduce some colors available in other. Because of that, and because both color spaces achieve their colors through entire different method (RGB is additive and CMYK is subtractive) the colors you get when switching color mode in document will be made as close to original as possible - but not identical.
If you want a coherent color scheme in your identification system, you must select it at first, and find equivalents in other color spaces prior to working with them. That way, you'll be sure your color scheme stays the same throughout your entire work.
There is a lot of debate whether documents for print should be prepared in RGB or CMYK colorspace - some newer printers do work on RGB colorspace and try to preserve colors when printing, but in my experience and because most printing offices that I work with don't use state-of-the-art modern machines I've learned that if I want some color in print to appear as I've designed, I should make it a CMYK one.
It's easy, In Photoshop specifically. You save your edited photo as .psd file, then change the photo Mode from RGB to CMYK, but before this converting, you are asked to rasterize the image and flatten all layers, so you'll lose your original work and image. When the image is rasterized and flatten, then go again in section "Image" than "Mode" and change your RGB image to CMYK... without losing any colors!
I was playing with this problem and I find this way to solve it.
Good Luck! 😉