Recipients of my gmail don't see my address
They are almost certainly seeing the name you entered for yourself in settings. To fix this:


Open System Preferences app.
Tap on Mail, Contacts, Calendars.
Tap on the account you are having the problem with.
Tap where it says "Account" followed by your email address and a right-facing arrow.
In the first box, "Name", it probably says Gmail. Change it to what you want to appear in your return emails.