1st you need to setup your domain name MX records to point to your custom google email.
It's free :
Select Standard from the Apps Editions
Then click on get started,
you will be prompted with a field to enter your domain name :
Follow the instructions from there. Google covers every major Domain registrar on how to Edit your MX records.
once you verify your domain, Activate the Email service and add a new user. In this case will create firstname.lastname@example.org So all of the administrative emails generated by xenforo will be sent from that email : email@example.com
Then logon to your XenForo admin panel and select the option tab
Then select Email options :
Then finally setup your xenforo to use google SMTP Like this
Make sure you enter firstname.lastname@example.org complete (the whole email string) your password you just setup with google apps.
The port is 465 or 587
Click save and happy emailing
This way you avoid having your emails flagged as spam on your users end.
Let me know if further help is needed.