How do I deactivate my Apple ID?

See -> How to deactivate your Apple ID account

How to deactivate your Apple ID account – Apple Support (UK)

Scroll to ->  How to temporarily deactivate your Apple ID

Sign in to your Apple ID account page on a Mac, PC, iPhone, or iPad. Then scroll down to Data and Privacy, and select "Manage your Data and Privacy." On the following page, select "Get started" under "Deactivate your account." If you don’t see this option, it means that this feature is not available in your country or region. 

👉 When you request to deactivate your account, you receive a unique alphanumeric access code. Make sure that you keep this access code in a safe place—you must have it to reactivate your account. 

If you forgot the access code, try to contact Apple Support -> Get Support (apple.com)

 Do you want to change your Apple ID email address on your current Apple ID so you retain access to your data and prior purchases? Note the restrictions in the article.

Apple ID Name Change.  * 

Make sure you turn off Find My Phone before signing out of the old ID. Once signed out and Find My Phone is off, then sign in with the new ID, then turn Find My Phone back on.

 What to do after you change your Apple ID or password - Apple Support  *  I suggest doing this before you change your Apple ID or password.

or is the Gmail account not your Apple ID address?

Apple ID email addresses.