Just because you use Gmail for
receiving mail doesn't mean you need to use it for
sending mail. You could remove the
relayhost configuration setting and just have Postfix directly deliver mail to its destination. You would want to set
inet_interfaces = loopback-only so that Postfix would not accept mail from outside.
If you have reasons for relaying through Gmail, It's possible that's just the way it works, using your source IP address and forcing the From e-mail address to match the one you have registered. Have you set your
smtp_sasl_password_maps in Postfix to use your username and password when sending mail? That might (or might not) change Gmail's behavior. (I don't use Google e-mail so this is mostly guesswork.)