You do not have to remove your tag when you goto other servers unless either 1) they require it, 2) you just want to, or 3) you plan on (and i hope this isn't the case) doing something that is less than eGO appropriate.
Now noone excepts you to be a saint all the time (god knows i'm not) however, >IF< you are going to other servers for any reason that may be considered offensive, or griefing or whatever it is you want to do. i only give you one piece of advice (read: ya better do it) Change your name >BEFORE< you enter the server. Because if you act like a total jerk, while wearing our tag, and someone sees it. then we will have to "talk to you" Now that is not a threat, or in anyway meant to differ you from having a good time in other servers. just do yourself a favor (and eGO) and remove the tag before you join the server if you plan on acting non-eGOish*
Because if you join, and then change the name, there is a log of it on their servers. and remember there are some people out there, that don't like us, and nothing would bring them greater satisfaction to report you.
Anyway i hope the information in here has cleared up your question, and if you have any more, feel free to add me to steam friends (link in my signature) and i will do my best to help you :">
*Think of it this way (and someone made a perfect example of this in our admin forums): I work for the state government, and i wear a uniform, when i wear that uniform no matter WHERE i am, i am representing my government. So i MUST act accordingly. If i want to let loose, unwind, go act a fool in public, i go home. take off my uniform and THEN go do whatever it is i'm going to do.