How can I change the color on my name/picture in lobby and games?
I don't think you can change the actual colors in the settings. You can turn them off or select a preferred color in the lobby, but without going into the files and changing it manually (which i don't recommend) it isn't possible.
EDIT: Here are the patch notes from when the teammate colors were introduced. There is no mention of an option to change it in this or future patch notes.
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1Regarding your answer: Do you think you'd be able to provide an official source? We tend to reward answers that have a good bit of research behind them rather than speculation. – Ave Aug 24 '15 at 7:39
You can create a lobby, right click on your picture* and change color. It'll stay in that color in that lobby & the games you enter with that lobby. If you aren't 5/10 (5 for Competitive, 10 for Casual) in a lobby and somebody else selected same color too (in another lobby), your or his/her color will be random.
//add this to your autoexec.cfg... create file if it does not exist in steam_folder/steamapps/common/Counter-Strike Global Offensive/csgo/cfg)
cl_color 0 // for yellow, cl_color 1 = purple, cl_color 2 = green, cl_color 3 = blue, cl_color 4 = orange
host_writeconfig // if that doesn't set it, run exec autoexec.cfg from console and restart
Enter this in console and restart Counter Strike: GO:
cl_color 10 0 0
You will be bot colours.