Support

No, it is not possible to hide backup profiles or otherwise make them available only to specific administrators. You can, however, give non-Super Users the akeeba.backup privilege without the akeeba.configure or akeeba.download privileges to make sure they can take backups without being able to see / change the configuration of the backup profiles or download / restore backups respectively. 

The other possibility is for us to give each backup profile a View Level to let you show / hide it based on Joomla's view access levels. Even in this case it would be cumbersome. For most of our users we'd have to set the access to Public to allow any user with Akeeba Backup usage privileges to use the backup profiles. In your use case you'd have to set up a group and access level and assign only your user to that group. However, this doesn't exactly protect you from other Super Users or even simple Managers and Administrators; they could simply assign themselves to your special group to get access to that backup profile. It also creates several complications such as what happens if you have a menu item or the backup-on-update use a profile the current user does not have access to. Do we still take the backup or do we fail? What happens if you change the access to the default profile, leaving Akeeba Backup without a safe fallback? These reasons and the fact that your use case is very uncommon make it extremely unlikely that we will ever implement such a feature.