Specify 'From' address for customer notifications on a Case Comment

• If the contact on the case is not a member of any portal. Then the from address is the email of the user that entered in the case comment. It is only possible to send the notification to non-portal users if the 'Enable Case Comment Notification to Contacts' checkbox is checked-

In CLASSIC: Setup | Customize | Cases | Support Settings

In LIGHTNING:  Setup | Feature Settings | Service | Support Settings
 

• However, if you have the 'Send Case Notifications from System Address' checkbox selected, then the from email address, displayed on case comment, attachment, and assignment notifications sent to case owners, will be noreply@salesforce.com. See this article for more on this functionality  - Customizing Support Settings

In CLASSIC: Setup | Customize | Cases | Support Settings

In LIGHTNING: Setup | Feature Settings | Service | Support Settings
 

• If the contact on the case is a self-service user then the from address can be specified by going to your self-service portal settings: Setup | Customize | Self-Service | Self-Service Portal | Settings | Self-Service Setup. Here you can enter the email address and its name in the 'Email Notifications Settings' section.

NOTE: Available in: Salesforce Classic
 

• Starting with Spring ’12, the Self-Service portal isn’t available for new orgs. Existing orgs continue to have access to the Self-Service portal.
• If the contact on the case is a customer portal user then the address can be specified by going to your customer portal settings: Setup | Customize | Customer Portal | Settings | Click on the name of your customer portal. Here you can also enter the mail address and its name in the 'Email Notifications Settings' section.

• If the contact on the case is a partner portal user then the address can be specified by going to your customer portal settings: Setup | Customize | Partners | Settings | Click on the name of your partner portal. Here you can also enter the mail address and its name in the 'Email Notifications Settings' section.

• If the contact on the case is a Community User then the address can be specified by going to your Community settings: 

In CLASSIC: Setup | Customize | Digital Experiences | All Sites| Click Workspaces next to the Community and Administration | Emails

In LIGHTNING:  Setup | Feature Settings | Digital Experiences | All Sites | Click Workspaces next to the Community and Administration | Emails

Under Sender, modify the field "email address". 

See Also:

Enable Self-Service Features and Settings
Associate a Portal with Salesforce Sites