iPhone Mail or GMail apps settings for Gmail label notification
Presuming you are a free gmail account I don't think it is possible in either the mail or Gmail app.

It's possible using Exchange ActiveSync and the mail app but Google hasn't allowed this to be setup since 2013 for free Gmail accounts.

It should be possible if you are a google apps user.

Apple's instructions for setup for exchange account in mail.

Once the account is set up go to "Fetch New Data" in Settings > Accounts and Passwords. Click the account and select the mailboxes to be pushed.