However, you may want to not be disturbed and still want to be notified when you get calls from specific people. There's a way to do this, but it's a bit complex; a Stack Exchange member explained how to do it.
It involves creating a group for the person or people you want to "disturb" you in Contacts (either on your Mac or on iCloud.com; you can't do this on the iPhone), and selecting that group in Settings > Notifications > Do Not Disturb. You can choose to allow calls from Everyone, No One, Favorites, or specific groups. So you might have a few people set as Favorites, so you can call them quickly from the Phone app, but if you want to limit the rings to just one or two people, it's easier to create a group for them.
See the Stack Exchange post for details on creating groups in Contacts.

