Google Account Email Address is NOT My Gmail, Gmail App Issue

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http://forums.androidcentral.com – This is my first android phone, SPrint Galaxy Note 2. My Google Account thus the play store email address is not associated with any gmail email, and I do have a few gmail accounts I want to put in to the stock gmail app. Problem is when I try to start the stock gmail app, it wants to automatically attach to my Google Account email. Can I delete the app and re-install? How can I run at least 1 gmail account inside the Gmail app when that gmail account is NOT the phone's Google Account email? Thanks. (HowTos)