Missing customer info in orders

Hi,

Custom user fields are attached to the user not to the order.
They display on the user registration form on the checkout because that's where you want the user to be able to fill his custom user fields. They can then edit them in their Joomla profile if you give them access to the fields there.
But it's normal that these fields are not displayed in the emails.
If you want custom fields that need to be filled during the checkout and that are attached to the order and added in the emails automatically, you can instead use custom fields of the table "order".

Otherwise, with custom user fields, if you want them to appear in the emails, you'll have to edit the emails in the menu System>Emails and modify the code of the email. For example, in the html version, you could add {VAR:user.phone_number}

Also, I would recommend against using the column name "name" for your custom user field because a column with the same name is already used by Joomla and when the user data is loaded with the same query, your value might be overwritten by the one in Joomla.