You need to edit your config_mp file with text editor like WordPad / NotePad(++). You can find the file in your Black Ops game foder, press Windows button + R and type in this following path:
C:\Program Files (x86)\Steam\steamapps\common\call of duty black ops\players
Now open the config_mp with text editor, if you can search, then search customclass if you can search stuff, then find this
There you will find the name of your first customclass. To change the color add ^ and the color number/character of your choice infront of it. Do this to all of the 5 customclasses.
To change the name of the customclasses you have achieved as prestige reward you need to search again, now search for prestigeclass1. That will be your first prestige class. Do the same as above for them.
Here are the colors available for use: ^1 RED
^2 GREEN
^3 YELLOW
^4 BLUE
^5 TEAL
^6 PINK
^7 WHITE (cant make white text or it would not show) xD
^8 GREY
^9 BROWN
^0 BLACK
^@ BROWN-ORANGE
^= LIGHTER BLUE
^; DARKER GREEN
^: DARKER RED
^> LIGHTER GREY
^< ORANGE
^? PURPLE