BlaneckW: Someone has already asked this question, it is in another thread dedicated to the same question. If you find it, post the link here for the next person who wants other people to do their work for them.
Thanks for the help (not), but I did find that thread you were talking about!
Here it is for anyone who has the same problem:
Basically, you go to the directory that you installed SimCity 2000 to (usually C:\GOG Games\SimCity 2000 Special Edition). You then click on the program called loader(dot)exe and type in the name and organisation you want to use (you can leave the organisation blank if you wish). Click ok, and the program will close. The next time you open simcity 2000 you should see your name as the mayor name.
If you decide that you want to change the name again, go to the file named loader(dot)ini , and open it with notepad. Where it says 'RunOnce=1', replace the '1' with '0'. You should be able to run the again and change your name/organisation again.