The title says it all, really. I'm Alice, and I want to login to Gmail's web interface through my browser. Ike, the internet service provider, and Adam, the local network administrator, would like to know what my Gmail email address (username) is. Is there any conceivable way for things to happen so that either one of them could possibly learn it?
For your average home user, services like GMail (that are run over TLS) would not leak information like the username to the ISP or network administrator.

If you're using a machine that is also administered by the LAN administrator (e.g., a work computer attached to a domain run by the company), then you have to assume they can read anything you do on it.  They could have software to log your activity (browsing and/or keystrokes), they could have installed extra SSL certificates that allow them to MITM your connection to GMail (or any other site).

If you believe your computer has not been tampered with and is not under the control of someone you don't trust (i.e., the LAN admin doesn't control your machine), then you can connect to GMail over https.  (At this point, the LAN admin is equivalent to an attacker on the internet.)  Ensure that you connect to https://mail.google.com with a valid certificate, and then all your traffic between your computer and the GMail servers are encrypted.  This would include all information about your account, including the username with which you are logged in.
