As far as I know, for TF2 you have to change your Steam display name (and remember to just put the e, as eGO indicates an admin). For the ™, there is a number code for it, but copying and pasting is probably easier. Also, you didn't ask and I'm not sure, but I don't think having a space after the tag matters.
edit: Tiddy posted while I was typing. Remember to watch out for eGO ninjas.
To my understanding is that you are promoted and then receive a G and then promoted again for the O...if your name does not appear here, then you are an e for the meantime until you get promoted. Not sure how often promotions happen, but one was given out yesterday, as far as asking for a promotion I beleive you click on mygroups and choose a TF2 group to join and an admin will respond.
The hardest part is the trademark symbol. You can either copy and paste it or, while holding down Alt in Notepad, type 0158.
1. Open Steam
2. Hit File -> Settings
3. Hit the Friends tab at the top
4. Change your nickname: =(e)=™ Sigmar228
5. Get in the game and start blowing things up!
Be active on the forums, follow the rules and help others in the servers when you can. Attend meetings and events. Have fun when you play. Do not ask for admin.