There are several ways to change your username:
TS3
When you are already connected:
Double clock your name to temporarily change the displayed name:
Before you connect:
Enter the desired username in the nickname field:
In your bookmarks:
Hit Ctrl + B to open your bookmarks -> select the one you want to edit and change the nickname:
Of the hole identity (globally)
Hit Ctrl + I to open your identities -> select the one you want to edit and change the nickname:
TS5
When you are already connected:
Right click on your name in the server tree to open the context menu.
On the top right click on the pencil icon to change the current username:
Press Enter to keep the changes
Before you connect:
This is not possible in TeamSpeak 5 - the identity name will be used!
In your bookmarks:
Right click the bookmark and select Edit.
There you can just enter the desired nickname and save it by pressing anywhere.
Of the hole identity (globally)
Open the settings (next to the search bar) -> go to Identities.
Select the identity you want to change and enter the new nickname:
The account name (e.g. used for the new chat feature)
Open the settings (next to the search bar) -> go to Account.
Enter the new nickname next to the client icon in the top left corner:
Website
It is (currently) not possible to even change the account name on the myteamspeak website.
I hope this covered all possible ways to change the nickname anywhere 