Hi Matt,
The activity notifications are sent using actions on the Save buttons. If you edit the save button and take a look at the actions, you'll see conditional statements that check to see if the user has checked the send email notification option. If this is checked, another action set is called that sends the email.
Now going back to your goal of changing the the email template, the action set that sends the email uses something called merge fields. Merge fields is a character function that allow you to replace fields in the email template with specific values from a table depending on what is being called (ie. the contact name from the Contacts table). In your case, you'll want to modify the email template to include a merge field for the company name. You can find more info about merge fields on our Help Center. Below is an example of how merge fields are used to change the values in an email:
In the above example, this action is replacing the email subject with a value from the Activity table. A merge field consists of a table name and field name (Contacts.FirstName as an example). When used with the character function is replaces Contacts.FirstName with the actual first name of the recordID being used on the screen.
Hope this helps.
- Adam